How do you divide \frac { ( m ^ { 8} n ) ^ { - 8} } { m ^ { - 49} n ^ { 4} }?

2 Answers
Jul 22, 2017

Simple. Distribute the exponent to the terms in the parentheses and use the negative exponent property and add the corresponding terms together to simplify.

Explanation:

(m^8n)^-8/(m^-49n^4)

Distribute the exponent to the terms in the parentheses.

=(m^-64n^-8)/(m^-49n^4)

Move the negative exponents and simplify by crossing out the corresponding terms.

=m^49/(m^64n^12)

=1/(m^15n^12)

Jul 22, 2017

1/(m^15n^12)

Explanation:

Get rid of the bracket first by multiplying the indices.

\frac { ( m ^ { 8} n ) ^ { - 8} } { m ^ { - 49} n ^ { 4} }

=\frac { m ^ { -64} n^-8} (m ^ { - 49} n ^ { 4})

Recall the law: " "x^-m = 1/x^m and 1/y^-n = y^n

Change negative indices to positive indices

m^49/(m^64n^4n^8)

Subtract the indices on m to get positive indices.
Add the indices of n

1/(m^15n^12)