Question

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

Answer 1

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

Answer 2

`\boxed{ (1)/(5^(12)) * (1)/(32^(3)) * (1)/(9^(15))}`

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) * 32^(-3) * 9^(-15)`

Changing the terms into it's reciprocal form:

`\implies (1)/(5^(-12)) * (1)/(32^(-3)) * (1)/(9^(-15))`

Changing the signs of the exponent:

`\implies\boxed{ (1)/(5^(12)) * (1)/(32^(3)) * (1)/(9^(15))}`