Question

How could you have simplified problem 7 in a different way?

Answer 1

The simplified form of
`((7^(-3)*3^(-8) )/(7^(-2)*3^(-2) ) )^(-4)` is
`7^(4) * 3^(24)`.

Explanation:

Here, the given problem is in exponential form with the power of -4.

The question is to simplify
`((7^(-3)*3^(-8) )/(7^(-2)*3^(-2) ) )^(-4)`

The first step in the simplification process is to multiply the power -4 outside the bracket with each powers inside the bracket.

⇒
`((7^(12)*3^(32) )/(7^(8)*3^(8) ) )`

Now, split them into two separate terms.

⇒
`((7^(12) )/(7^(8) ))`
`((3^(32) )/(3^(8) ) )`

We know that, the division in the exponential rule with same base is given by ⇒
`(a^(m) )/(a^(n) ) = a^(m-n)`

⇒
`7^(12-8)* 3^(32-8)`

⇒
`7^(4) * 3^(24)`

Therefore, the simplified form of
`((7^(-3)*3^(-8) )/(7^(-2)*3^(-2) ) )^(-4)` is
`7^(4) * 3^(24)`.