Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. $$\left( \frac { 81 s ^ { 12 } r ^ { - 4 } } { 16 s ^ { - 4 } r ^ { 4 } } \right) ^ { 3 / 4 }$$
A) $\frac { 3 s ^ { 12 } } { 2 r ^ { 6 } }$
B) $\frac { 27 s ^ { 6 } } { 8 }$
C) $\frac { 3 s ^ { 16 } r ^ { 8 } } { 2 }$
D) $\frac { 27 s ^ { 12 } } { 8 r ^ { 6 } }$

Question

Quizplus · Accepted Answer

First, simplify the fraction inside the parentheses: $\frac{81s^{12}r^{-4}}{16s^{-4}r^4} = \frac{81}{16}s^{12-(-4)}r^{-4-4} = \frac{81}{16}s^{16}r^{-8}$. Then, apply the exponent $\frac{3}{4}$ to each part: $\left(\frac{81}{16}\right)^{\frac{3}{4}}s^{16\cdot\frac{3}{4}}r^{-8\cdot\frac{3}{4}} = \frac{27}{8}s^{12}r^{-6}$, which simplifies to $\frac{27s^{12}}{8r^6}$.

Simplify the Expression by Using the Properties of Rational Exponents (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

Simplify the Expression by Using the Properties of Rational Exponents $\left( \frac { 81 s ^ { 12 } r ^ { - 4 } } { 16 s ^ { - 4 } r ^ { 4 } } \right) ^ { 3 / 4 }$