Question

Blake simplified the expression ((x^12)/(x^-3))^5 to 1/x^20. What was his mistake?

a) He added 5 to the exponent in the numerator instead of multiplying.

b) He subtracted the exponents in the parentheses instead of dividing.

c) He multiplied only the exponent in the numerator of the fraction by 5.

d) He divided the exponents in the parentheses instead of subtracting.

Answer 1

d) He divided the exponents in the parentheses instead of subtracting

Explanation:

First you should know that the power of a power based

"a" is the power based on "a" and whose exponent is the product of the exponents:

`(a^(n))^(m)=a^(n*m)`

By simplifying the expression you get,

`((x^(12))^(5))/((x^(-3))^(5))=(x^(12-(-3)))^(5)=(x^(12+3))^(5)=(x^(15))^(5)=x^(15*5)=x^(75)`

What Blake did wrong is what says option d) He divided the exponents in the parentheses instead of subtracting.

This is what he did wrong:

`((x^(12))^(5))/((x^(-3))^(5))=(x^(12/(-3)))^(5)=(x^(-4))^(5)=x^(-4*5)=x^(-20)=(1)/(x^(20))`

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Hope this helps!