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

Question

1483 views around the world

You can reuse this answer
Creative Commons License

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: $x^-m = 1/x^m$

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

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

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