Select the equivalent expression. $\newline$ $\left(\frac{3^{6}}{y^{-5}}\right)^{2}=\,?$ $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{3^{6}}{y^{-10}}$ $\newline$ (B) $3^{12}y^{10}$ $\newline$ (C) $\frac{3^{12}}{y^{-5}}$

Full solution

Q. Select the equivalent expression.

\newline

\left(\frac{3^{6}}{y^{-5}}\right)^{2}=\,?

\newline

Choose

1

answer:

\newline

(A)

\frac{3^{6}}{y^{-10}}

\newline

(B)

3^{12}y^{10}

\newline

(C)

\frac{3^{12}}{y^{-5}}

Apply power of power rule: Apply the power of a power rule. $\newline$ The power of a power rule states that $(a^{m})^{n} = a^{m*n}$ . We will apply this rule to both the numerator and the denominator separately. $\newline$ $\left(\frac{3^{6}}{y^{-5}}\right)^{2} = \frac{3^{6*2}}{y^{-5*2}}$
Calculate exponents: Calculate the exponents. $\newline$ Now we will calculate the exponents for both $3$ and $y$ . $\newline$ $3^{(6*2)} = 3^{12}$ $\newline$ $y^{(-5*2)} = y^{-10}$
Rewrite expression with calculated exponents: Rewrite the expression with the calculated exponents. $\newline$ The expression now becomes: $\newline$ $(3^{12})/(y^{-10})$
Simplify expression: Simplify the expression. $\newline$ Since $y^{-10}$ is in the denominator, we can move it to the numerator to make the exponent positive. $\newline$ $(3^{12})/(y^{-10}) = 3^{12} \cdot y^{10}$
Choose correct answer: Choose the correct answer. $\newline$ The simplified expression is $3^{12} \times y^{10}$ , which corresponds to answer choice $(B)$ .