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)#