How do you simplify #(5b^-3)^4# and write it using only positive exponents?

2 Answers
Aug 30, 2016

Answer:

#=625/b^12#

Explanation:

#(5b^-3)^4#

#=(5/b^3)^4#

#=625/b^12#

Aug 30, 2016

Answer:

#5^4/b^12 = 625/b^12#

Explanation:

There are 3 laws of indices being applied here,

A power outside applies to all the factors inside: #(xy)^m = x^my^m#

Raising to a power, multiply the indices: #(x^m)^n = x^(mn)#

Negative index becomes positive in the denominator and v.v.

#x^-m = 1/x^m# or #1/x^-n = x^n#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#(5b^-3)^4 = 5^4 b^-12#

#= 5^4/b^12#

This can also be written as #625/b^12#