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

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Answer 1 · 2016-08-30T11:35:16

#=625/b^12#

#(5b^-3)^4#

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

#=625/b^12#

Answer 2 · 2016-08-30T11:45:59

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

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#