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

Apr 29, 2017

$\frac{1}{m} ^ 2 \cdot {n}^{\frac{10}{3}}$

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.

${\left(m \cdot {m}^{-} 2 \cdot {n}^{\frac{5}{3}}\right)}^{2}$
${\left(= {m}^{1 + \left(- 2\right)} \cdot {n}^{\frac{5}{3}}\right)}^{2}$
$= {\left({m}^{- 1} \cdot {n}^{\frac{5}{3}}\right)}^{2}$

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.

${m}^{\left(- 1\right) \cdot 2} \cdot {n}^{\frac{5}{3} \cdot 2}$
$= {m}^{- 2} {n}^{\frac{10}{3}}$

Give the answer with positive indices.

$= \frac{1}{m} ^ 2 \cdot {n}^{\frac{10}{3}}$

I hope that helps!