How do you simplify #(-2x^2)^3(4x^3)^-1 #?

1 Answer
Jul 11, 2016

Answer:

#-2x^3#

Explanation:

Rule #1:

#(a^b)^c = a^(b*c)#

Rule #2

#a^-1 = 1/a#

Rule #3

#(a^b)/(a^c) = a^(b-c#

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#(-2x^2)^3(4x^3)^-1#

Use rules #1# and #2# (mentioned above) of exponents

#(-2^3x^(2*3))(1/(4x^3))#

Simplify by multiplying out the exponents

#(-8x^6)(1/(4x^3))#

Write as fractions

#(-8x^6)/1 * 1/(4x^3)#

Rewrite as a single fraction

#((-8x^6)times1)/(1times(4x^3))#

Multiply numerator and denominator by #1#

#(-8x^6)/(4x^3)#

Simplify coefficients and then simplify variables using rule #3# from above

#(-2x^3)/1#

Write without a denominator

#-2x^3#