Write the word or phrase that best completes each statement or answers the question.
Write the expression by using rational exponents rather than radical notation.
-$$\left( \frac { 81 s ^ { 12 } r ^ { - 4 } } { 16 s ^ { - 4 } r ^ { 4 } } \right) ^ { 3 / 4 }$$
A) $\frac { 27 s ^ { 6 } } { 8 }$
B) $\frac { 27 s ^ { 12 } } { 8 r ^ { 6 } }$
C) $\frac { 3 s ^ { 16 } r ^ { 8 } } { 2 }$
D) $\frac { 3 s ^ { 12 } } { 2 r ^ { 6 } }$

Question

Quizplus · Accepted Answer

First, simplify the expression inside the parentheses by dividing the numerators and denominators and subtracting the exponents: $\frac{81}{16} = 3^4$, $s^{12 - (-4)} = s^{16}$, and $r^{-4 - 4} = r^0 = 1$, giving $(3^4 s^{16})^{3/4}$. Applying the exponent, $3^3 = 27$, $s^{16 \cdot 3/4} = s^{12}$, and since $r^0 = 1$, it does not appear in the final expression. Thus, the correct expression is $\frac{27 s^{12}}{8}$, which matches choice B.

Write the Word or Phrase That Best Completes Each Statement (81s12r−416s−4r4)3/4\left( \frac { 81 s ^ { 12 } r ^ { - 4 } } { 16 s ^ { - 4 } r ^ { 4 } } \right) ^ { 3 / 4 }(16s−4r481s12r−4​)3/4

Write the Word or Phrase That Best Completes Each Statement $\left( \frac { 81 s ^ { 12 } r ^ { - 4 } } { 16 s ^ { - 4 } r ^ { 4 } } \right) ^ { 3 / 4 }$