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

1 Answer
Anirudh E. · EZ as pi
Apr 29, 2017

# 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!

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