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

2 Answers
Peter L.
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)#

EZ as pi
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)#

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