Question

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

Answer 1

Answer:

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

Step-by-step 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,

$\frac{(x^{12})^{5}}{(x^{-3})^{5}}=(x^{12-(-3)})^{5}=(x^{12+3})^{5}=(x^{15})^{5}=x^{15*5}=x^{75}$

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:

$\frac{(x^{12})^{5}}{(x^{-3})^{5}}=(x^{12/(-3)})^{5}=(x^{-4})^{5}=x^{-4*5}=x^{-20}=\frac{1}{x^{20}}$

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Hope this helps!