Question

5^5(16^2*5^3)^3=?Rewrite the expression as a product of two powers and two quotients

Answer 1

We have the next expression:

`5^5(16^2\cdot5^3)^3`

Now, solve the parentheses using the next property:

`(a^m)^n=a^(m\cdot n)`

Therefore:

`(16^2\cdot5^3)^3=16^(2\cdot3)\cdot5^(3\cdot3)`
`=16^6\cdot5^9`

Which represents the product of two powers.

But, we need to find two quotients:

Then, we can rewrite the next expression:

`16^6=16^4\cdot16^2`

To make fractions, we use the next property:

`a^m=(1)/(a^(-m))`

Then:

`16^416^2=(1)/(16^(-4)16-^2)`

The result expression for the product of two powers:

`(5^2\cdot5^9)/(16^(-4)16-^2)`

The result for the product of two quotients:

`(16^4\cdot5^9)/(16^(-2)\cdot5^(-2))`