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.