Simplify the expression. Assume that variables represent nonzero real numbers. Write the answer using positive exponents only. $\left( \frac { a ^ { 2 } } { b ^ { 3 } } \right) ^ { - 5 }$
A) $\frac { b ^ { 15 } } { a ^ { 10 } }$
B) $- \frac { a ^ { 10 } } { b ^ { 15 } }$
C) $\frac { a ^ { 10 } } { b ^ { 15 } }$
D) $- \frac { a ^ { - 10 } } { b ^ { - 15 } }$
E) $\frac { b ^ { 10 } } { a ^ { 15 } }$

Question

Quizplus · Accepted Answer

When you raise a power to a power, you multiply the exponents. Here, $\left( \frac { a ^ { 2 } } { b ^ { 3 } } \right) ^ { - 5 }$ becomes $\frac { a ^ { 2 \cdot (-5) } } { b ^ { 3 \cdot (-5) } }$, which simplifies to $\frac { b ^ { 15 } } { a ^ { 10 } }$ because negative exponents indicate reciprocal powers.

Simplify the Expression (a2b3)−5\left( \frac { a ^ { 2 } } { b ^ { 3 } } \right) ^ { - 5 }(b3a2​)−5

Simplify the Expression $\left( \frac { a ^ { 2 } } { b ^ { 3 } } \right) ^ { - 5 }$