How do you simplify #(- 2) ^ { 7} \frac { 1} { 8} a ^ { - 5}#?

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Answer 1 · 2017-10-04T12:23:05

See a solution process below:

First, #(-2)^7# can be rewritten as: #-128# allowing us to rewrite the expression as:

#-128 * 1/8 * a^-5 =>#

#-16 * a^-5 =>#

#-16a^-5#

Or

#-(2^4)a^-5#

We can now use this rule for exponents to eliminate the negative exponent:

#x^color(red)(a) = 1/x^color(red)(-a)#

#-(2^4)a^color(red)(-5) =>#

#-(2^4)/a^color(red)(- -5) =>#

#-(2^4)/a^color(red)(5)# or #-16/a^color(red)(5)#