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

May 29, 2017

$= \frac{1}{x} ^ 20$

Explanation:

There are three laws of indices at play here.

• ${\left({x}^{a} \times {y}^{b}\right)}^{m} = {x}^{a m} \times {y}^{b m}$

• ${x}^{-} m = \frac{1}{x} ^ m$

• ${x}^{m} \times {x}^{n} = {x}^{m + n}$

It does not matter which law you apply first!

I will choose to get rid of the bracket by multiplying the indices.

${\left({x}^{-} 2 {x}^{-} 3\right)}^{4} = {x}^{-} 8 {x}^{-} 12$

Add the indices of like bases:

$= {x}^{-} 20$

$= \frac{1}{x} ^ 20$