How do you simplify #(x ^ { 5} y ^ { - 9} ) ^ { 3}#?

2 Answers
Daniel H.
Mar 3, 2018

Since the expression is inside parenthesis, the exponent 3 will affect the entire expression

Explanation:

In this form, the laws of exponents tell us #(a^xb^y)^n)=a^{nx}b^{ny}#

So, in your case #(x^5y^{-9})^3 -> x^{5*3}y^{-9*3}->x^15y^-27#

maganbhai P.
Mar 3, 2018

#x^15*y^(-27)#

Explanation:

#color(red)((1)(M*N)^Z=M^Z*N^Z)#
#color(red)((2)(A^M)^N=A^(MN))#
Here,
#(x^5*y^(-9))^3=(x^5)^3*(y^(-9))^3,# [Applying (1)]
#(x^5*y^(-9))^3=(x^((5)(3))*(y^((-9)(3))),# [Applying (2)]
#(x^5*y^(-9))^3=x^15*y^(-27)#

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