How do you simplify #[x^-9(81x^8)]^(5/4)#?

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Answer 1 · 2017-04-25T10:45:28

#=243/(x^(5/4)) = 243/(root4 x^5)#

Use the power law of indices - multiply the indices.

#[x^-9(81x^8)]^(5/4) " = "x^(-45/4) xx81^(5/4)x^10#

Recall: #color(red)(x^m xx x^n = x^(m+n))" and "color(blue)(x^(p/q) = rootq x^p)#

#color(red)(x^(-45/4)) xxcolor(blue)(81^(5/4))color(red)(x^10) = color(blue)(root4(81)^5)color(red)(x^(-5/4))#

Recall: #x^-m = 1/x^m#

#=color(blue)(3^5)/color(red)(x^(5/4))#

#=243/(x^(5/4))#