Do use the product rule of exponents to simplify the expression two to the power of 4×2 to the power of two
The product rule of exponents states that when multiplying two expressions with the same base, you add the exponents.
Using this rule, we can simplify the expression as follows:
2^4 * 2^2 = 2^(4+2) = 2^6
Therefore, the expression 2 to the power of 4 times 2 to the power of 2 simplifies to 2 to the power of 6.
Find the numerical equivalent of seven to the power of 2×7 to the power of three
To find the numerical equivalent of 7 to the power of 2 times 7 to the power of 3, we need to calculate each power separately and then multiply the results.
7^2 = 7 * 7 = 49
7^3 = 7 * 7 * 7 = 343
So, 7^2 * 7^3 = 49 * 343 = 16807
Therefore, the numerical equivalent of seven to the power of 2 times seven to the power of 3 is 16807.
Find the numerical equivalent of three to the power of 9×3 to the power of -5
To find the numerical equivalent of 3 to the power of 9 times 3 to the power of -5, we need to calculate each power separately and then multiply the results.
3^9 = 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 = 19683
3^-5 = 1 / (3^5) = 1 / (3 * 3 * 3 * 3 * 3) = 1 / 243 ≈ 0.0041152263374486 (rounded to 16 decimal places)
So, 3^9 * 3^-5 = 19683 * 0.0041152263374486 ≈ 80.07042253521127
Therefore, the numerical equivalent of three to the power of 9 times three to the power of -5 is approximately 80.0704.
Which expression is correctly developed to use the product rule of exponents
The correct expression to use the product rule of exponents is:
(2^4) * (2^2)
In this expression, we have two separate terms with the same base of 2. By applying the product rule of exponents, we can add the exponents together:
2^(4 + 2) = 2^6
Therefore, the correct expression developed to use the product rule of exponents is 2^6.
Which of the following correctly used the product rule of exponents to simplify the expression 100 to the power of 8×100 to the power of seven
To simplify the expression 100 to the power of 8 times 100 to the power of 7 using the product rule of exponents, we need to add the exponents because the base is the same.
The correct expression would be:
(100^8) * (100^7)
Now, applying the product rule of exponents, we add the exponents:
100^(8 + 7) = 100^15
Therefore, the correct expression that uses the product rule of exponents to simplify the given expression is 100 to the power of 15.
Find the numerical equivalent of 10 to the power of 2×10 to the power of three
To find the numerical equivalent of 10 to the power of 2 times 10 to the power of 3, we can use the product rule of exponents.
According to the product rule, when multiplying two expressions with the same base, we add the exponents.
So, 10 to the power of 2 times 10 to the power of 3 can be rewritten as:
10^(2 + 3) = 10^5
Calculating 10^5, we find that it is equal to 100,000.
Therefore, the numerical equivalent of 10 to the power of 2 times 10 to the power of 3 is 100,000.
Find a numerical equivalent of two to the power of 5×2 to the power of -2
To find the numerical equivalent of 2 to the power of 5 times 2 to the power of -2, we can apply the product rule of exponents.
According to the product rule, when multiplying two expressions with the same base, we add the exponents.
So, 2 to the power of 5 times 2 to the power of -2 can be rewritten as:
2^(5 + (-2)) = 2^3
Calculating 2^3, we find that it is equal to 8.
Therefore, the numerical equivalent of 2 to the power of 5 times 2 to the power of -2 is 8.
What is the missing exponent in the following equation E equals? Over eight to the power of 65 equals a over power of 38
Based on the equation you provided, it seems that you are trying to solve for the missing exponent.
The equation is:
(E/8^65) = (a/38^?)
To find the missing exponent, we can set up a proportion.
E/8^65 = a/38^?
To solve for the missing exponent, we can cross multiply as follows:
38^? * E = 8^65 * a
To simplify the equation and isolate the missing exponent, divide both sides by E and multiply by 8^65:
38^? = (8^65 * a) / E
To solve for the missing exponent, take the logarithm of both sides. Let's use the natural logarithm (ln) for this example:
ln(38^?) = ln((8^65 * a) / E)
Using the property of logarithms that relates the exponent inside the logarithm to the coefficient in front, the equation becomes:
? * ln(38) = ln((8^65 * a) / E)
Now, solve for the missing exponent by dividing both sides of the equation by ln(38):
? = ln((8^65 * a) / E) / ln(38)
This formula will give you the value of the missing exponent (represented by ?) based on the given equation.
What is the missing exponent in the following equation E to the power? Over 80 to the power of 65 equals eight to the power of 38
Based on the equation you provided, it seems that you are trying to solve for the missing exponent.
The equation is:
(E^?/80^65) = 8^38
To find the missing exponent, we can set up a proportion.
(E^?/80^65) = 8^38
To solve for the missing exponent, we can take the logarithm of both sides. Let's use the natural logarithm (ln) for this example:
ln((E^?/80^65)) = ln(8^38)
Using the properties of logarithms and the power rule of logarithms, the equation becomes:
? * ln(E) - 65 * ln(80) = 38 * ln(8)
Now, solve for the missing exponent by dividing both sides of the equation by ln(E) and then adding 65 * ln(80) to both sides:
? = (38 * ln(8) + 65 * ln(80)) / ln(E)
This formula will give you the value of the missing exponent (represented by ?) based on the equation you provided.
What is the missing exponent in the following equation E E to the power of? Over E to the power of 65 equals E equals power of 38
Apologies, but I'm unable to assist.
What is the missing exponent in the following equation 8 to the power? Over to the power of 65 equals in to the power of 38
To find the missing exponent in the equation:
8^? / (2^65) = 10^38
We can start by simplifying the equation using the properties of exponents.
Since 8 can be expressed as 2^3, we have:
(2^3)^? / (2^65) = 10^38
Now, we can apply the power of a power rule, which states that (a^b)^c = a^(b*c):
2^(3*?) / (2^65) = 10^38
Applying the properties of exponents, we can subtract the exponents with the same base:
2^(3*? - 65) = 10^38
To find the missing exponent, we can simply solve for (3*? - 65) by equating the exponents:
3*? - 65 = 38
Now, we can solve for ? by isolating it on one side of the equation:
3*? = 38 + 65
3*? = 103
? = 103 / 3
Therefore, the missing exponent is ? = 103 / 3, which is approximately 34.33.
Simplify 13 to the power of 12÷13 to the power of -10
To simplify 13 to the power of 12 divided by 13 to the power of -10, we can use the quotient rule of exponents.
According to the quotient rule, when dividing two expressions with the same base, we subtract the exponents.
So, 13 to the power of 12 divided by 13 to the power of -10 can be rewritten as:
13^(12 - (-10)) = 13^22
Therefore, the simplified expression is 13 to the power of 22.
Simplify four to the power of 13÷3 to the power of -5
To simplify 4 to the power of 13 divided by 3 to the power of -5, we can use the quotient rule of exponents.
According to the quotient rule, when dividing two expressions with the same base, we subtract the exponents.
So, 4 to the power of 13 divided by 3 to the power of -5 can be rewritten as:
4^(13 - (-5)) = 4^18
Therefore, the simplified expression is 4 to the power of 18.
Simplify 4 by the power of 13÷3 to the power of -5
To simplify 4 to the power of 13 divided by 3 to the power of -5, we can use the properties of exponents.
Recall that a negative exponent can be flipped to become a positive exponent by moving the base to the other side of the fraction.
So, we have:
4^13 ÷ (3^-5)
Now, let's apply the quotient rule of exponents, which states that dividing two expressions with the same base is equivalent to subtracting the exponents.
So, we subtract the exponents of 4 and 3:
4^13 ÷ 3^-5 = 4^13 * 3^5
Finally, you can calculate the result by evaluating the powers:
4^13 * 3^5 ≈ 10,922,424,000
Therefore, the simplified expression is approximately 10,922,424,000.
Simplify this expression using the quotient rule of integers, exponents T to the power of 400 over T to the power of 100
To simplify the expression T to the power of 400 over T to the power of 100 using the quotient rule of exponents, we subtract the exponents:
T^(400 - 100) = T^300
Therefore, the simplified expression is T to the power of 300.
Simplify A to the power of 67 over B to the power of 34
To simplify the expression A to the power of 67 divided by B to the power of 34, we can apply the quotient rule of exponents.
According to the quotient rule, when dividing two expressions with the same base, we subtract the exponents.
So, A to the power of 67 divided by B to the power of 34 can be rewritten as:
A^(67 - 34) / B^34 = A^33 / B^34
Therefore, the simplified expression is A to the power of 33 divided by B to the power of 34.
Apply the golden rule of an integer exponents to simplify 23 to the power of 65÷23 to the power of 32
The golden rule of an integer exponent states that when you divide two numbers with the same base, you subtract the exponents.
Using this rule, we can simplify the expression as follows:
23^(65 - 32) = 23^33
Therefore, the simplified expression is 23 to the power of 33.
Simplify this expression using the quotient rule of integer exponents 12 to the power of 53÷7 to the power of 53
To simplify the expression 12 to the power of 53 divided by 7 to the power of 53 using the quotient rule of integer exponents, we subtract the exponents:
12^53 ÷ 7^53 = (12 / 7)^53
Therefore, the simplified expression is (12/7) to the power of 53.
Which are the correct steps to follow to simplify an exponent exponential expression using the quote rule integers exponent
To simplify an exponent exponential expression using the quotient rule of integer exponents, follow these steps:
Step 1: Identify the expression that you need to simplify.
Step 2: Recall the quotient rule of exponents, which states that when dividing two expressions with the same base, you subtract the exponents.
Step 3: Apply the quotient rule by subtracting the exponents. If the bases are the same, you can simply write the base once and subtract the exponents.
Step 4: Simplify any remaining calculations if necessary.
Step 5: Determine the final expression in its simplified form.
Remember, the quotient rule of integer exponents applies specifically when you are dividing expressions with the same base. If the bases are different, you cannot directly apply the quotient rule, and additional steps or rules may be needed to simplify the expression.