Which of the following correctly used the Product Rule of Exponents to simplify the expression 100*8 X 100*7 pls explain
To simplify the expression 100^8 * 100^7 using the Product Rule of Exponents, we add the exponents together.
The Product Rule of Exponents states that when multiplying two numbers with the same base, you add the exponents.
In this case, the base is 100.
So, 100^8 * 100^7 can be simplified as 100^(8+7).
Adding the exponents, we get 100^15.
Therefore, the expression is simplified as 100^15.
Question
Find the numerical equivalent of 10*2 ⋅10*3
To find the numerical equivalent of 10^2 * 10^3, we can apply the Product Rule of Exponents.
The Product Rule of Exponents states that when multiplying two numbers with the same base, you add the exponents.
In this case, the base is 10.
So, 10^2 * 10^3 can be simplified as 10^(2+3).
Adding the exponents, we get 10^5.
Therefore, the numerical equivalent of 10^2 * 10^3 is 100,000.
Find the numerical equivalent of 4*9⋅4*−7
To find the numerical equivalent of 4^9 * 4^(-7), we can again apply the Product Rule of Exponents.
The Product Rule of Exponents states that when multiplying two numbers with the same base, you add the exponents.
In this case, the base is 4.
So, 4^9 * 4^(-7) can be simplified as 4^(9+(-7)).
Adding the exponents, we get 4^2.
Therefore, the numerical equivalent of 4^9 * 4^(-7) is 16.
Which expression is correctly developed to use the Product Rule of Exponents?
10^8⋅10^8
6^2⋅7^3
The expression that is correctly developed to use the Product Rule of Exponents is:
10^8 * 10^8.
This expression is correct because both terms have the same base (10), and according to the Product Rule of Exponents, when multiplying two numbers with the same base, we add the exponents. In this case, the exponents are both 8, so we can simplify the expression by adding the exponents: 10^(8+8) = 10^16.
Apply the Quotient Rule of Integer Exponents to simplify 23^65÷23^32
.
The Quotient Rule of Exponents states that when dividing two numbers with the same base, you subtract the exponents.
In this case, the base is 23.
So, to simplify 23^65 ÷ 23^32, we subtract the exponents: 65 - 32.
This equals 23^33.
Therefore, the simplified expression is 23^33.
Question
Which are the correct steps to follow to simplify an exponential expression using the Quotient Rule of Integer Exponents?
To simplify an exponential expression using the Quotient Rule of Integer Exponents, follow these steps:
1. Identify the base: Identify the common base in the expression. This is the number that is raised to a power.
2. Determine the quotient: Subtract the exponent of the denominator from the exponent of the numerator.
3. Simplify: If the quotient is positive, rewrite the expression using the base and the simplified exponent. If the quotient is negative, take the reciprocal of the expression with the base and change the exponent to positive.
4. Calculate: Evaluate the expression to obtain the numerical value if necessary.
By following these steps, you can simplify an exponential expression using the Quotient Rule of Integer Exponents.
Which are the correct steps to follow to simplify an exponential expression using the Quotient Rule of Integer Exponents?
Responses
Check if the bases are different; if they are, subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Check if the bases are different; if they are, subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form. - incorrect
Subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form. - no response given
Check if the bases are the same; if they are, add the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
Check if the bases are the same; if they are, add the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form. - no response given
Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form. - not selected, this is the correct answer
The correct steps to follow to simplify an exponential expression using the Quotient Rule of Integer Exponents are:
1. Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as-is otherwise).
2. Write the resulting expression in exponential form.
So, the correct response is:
Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
Question
Which of the following shows the correct process of solving −4(3+12^0)+15^0
by generating an equivalent expression using the Zero Power Rule?
To solve the expression -4(3+12^0) + 15^0 by generating an equivalent expression using the Zero Power Rule, we need to simplify any exponent with a value of 0.
The Zero Power Rule states that any number (except 0) raised to the power of 0 is equal to 1.
The correct process to solve -4(3+12^0) + 15^0 using the Zero Power Rule is as follows:
1. Simplify the exponent of 12^0: 12^0 = 1.
2. Simplify the exponent of 15^0: 15^0 = 1.
3. Substitute the simplified values back into the expression: -4(3+1) + 1.
4. Continue to simplify the expression: -4(4) + 1.
5. Execute the multiplication: -16 + 1.
6. Complete the addition: -15.
Therefore, the correct equivalent expression using the Zero Power Rule is -15.