Apply the quotient rule of integer exponents to simplify 23⁶⁵ ÷ 23³².
A. 1³³
B. 23³³
C. 97
D. 23⁹⁷
To simplify 23⁶⁵ ÷ 23³² using the quotient rule of integer exponents, we subtract the exponents.
23⁶⁵ ÷ 23³² = 23^(65-32) = 23³³
So the correct answer is B. 23³³.
Simplify this expression using the quotient rule integer exponents 12⁵³ ÷ 7⁵³
A. 12¹⁰⁶
B. 12⁵³ ÷ 7⁵³
C. 5⁵³
D. 5¹⁰⁶
To simplify 12⁵³ ÷ 7⁵³ using the quotient rule of integer exponents, we subtract the exponents.
12⁵³ ÷ 7⁵³ = 12^(53-53) ÷ 7^(53-53)
= 12⁰ ÷ 7⁰
Since any number (except 0) raised to the power of 0 is 1, we have:
= 1 ÷ 1
= 1
So the correct answer is none of the given options.
To simplify the expression 23⁶⁵ ÷ 23³² using the quotient rule of integer exponents, we subtract the exponents.
The quotient rule states that when dividing two numbers with the same base, we subtract the exponent of the denominator from the exponent of the numerator.
In this case, we have 23 as the base, with an exponent of 65 in the numerator, and an exponent of 32 in the denominator.
Subtracting 32 from 65, we get 65 - 32 = 33.
Therefore, 23⁶⁵ ÷ 23³² simplifies to 23³³.
So, the answer is B. 23³³.
To apply the quotient rule of integer exponents, you can subtract the exponents of the same base.
In this case, you have 23 raised to the power of 65 divided by 23 raised to the power of 32.
Using the quotient rule, you subtract the exponents:
23^(65 - 32)
Simplifying further:
23^33
So the final answer is 23 raised to the power of 33.
Therefore, the answer is B. 23³³.