How do you simplify #ba^4*(2ba^4)^-3# and write it using only positive exponents?

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Answer 1 · 2017-02-17T02:40:48

The simplified answer is #1/(8b^2a^8)#.

Simplify #ba^4*(2ba^4)^(-3)#.

In order to simplify this expression, we will need to apply several rules of exponents.

Apply negative power rule #a^(-m)=1/am"#.

#(ba^4)/(2ba^4)^3#

Apply power rule #(a^m)^n=a^(m*n)#.

#(ba^4)/(2^3b^3a^12)#

Simplify #2^3#.

#(ba^4)/(8b^3a^12)#

Apply quotient rule #a^m/a^n=a^(m-n)#

#(b^(1-3)a^(4-12))/8#

Simplify.

#(b^-2a^-8)/8#

Apply negative power rule #a^(-m)=1/a^m#

#1/(8b^2a^8)#