Question

Rewrite the expression using only positive exponents. Show your work.

Answer 1

$5^{-12} \cdot 32^{-3} \cdot 9^{-15}\\\\\\=\dfrac 1{5^{12}} \cdot \dfrac 1{32^3} \cdot \dfrac 1{9^{15}}\\\\\\=\dfrac 1{5^{12}} \cdot \dfrac 1{(2^5)^3}\cdot \dfrac 1{9^{15}}\\\\\\=\dfrac 1{5^{12} \cdot 2^{15} \cdot 9^{15} }\\\\\\=\dfrac 1{5^{12}\cdot 18^{15}}$

Answer 2

Answer:

$\boxed{ \dfrac{1}{5^{12}} \times \dfrac{1}{32^{3}} \times \dfrac{1}{9^{15}}}$

Step-by-step explanation:

In this case, all the exponents are negative. To make them positive, take the term's reciprocal and change the exponents sign.

$\implies 5^{-12} \times 32^{-3} \times 9^{-15}$

Changing the terms into it's reciprocal form:

$\implies \dfrac{1}{5^{-12}} \times \dfrac{1}{32^{-3}} \times \dfrac{1}{9^{-15}}$

Changing the signs of the exponent:

$\implies\boxed{ \dfrac{1}{5^{12}} \times \dfrac{1}{32^{3}} \times \dfrac{1}{9^{15}}}$