Question

How do you simplify `(m*m^-2n^(5/3))^2`?

Answer 1

`1/m^2 *n^(10/3)`

Explanation:

According to the order of operations, parentheses are first. So, I am going to simplify what is inside the parentheses first. Remember to add the exponents of `m` since you are just multiplying with factors of `m`. The `n` stays the same.

`(m* m^-2 * n^(5/3))^2`
`(=m^(1 + (-2))* n^ (5/3) ) ^2`
`=(m ^(-1)*n^(5/3))^2`

Now, move on to the outside exponent since that is next in the order of operations. For this, you want to MULTIPLY the exponents, since power-of-a-power means multiplying the indices.

`m^((-1)*2)*n^(5/3 *2)`
`=m^(-2)n^(10/3)`

Give the answer with positive indices.

`= 1/m^2 *n^(10/3)`

And that would be your answer.

I hope that helps!