How do you simplify the expression (1/32)^(-2/5)?

1 Answer
Apr 20, 2016

(1/32)^(-2/5)=4

Explanation:

To make this easier to solve, there's a rule that helps: a^(mn)=(a^m)^n, and what it basically says is that you can split up to the index/exponent (the small raised number) into smaller numbers which multiply to it, e.g. 2^6=2^(2*3)=(2^2)^3 or 2^27=2^(3*3*3)=((2^3)^3)^3

Ok let's make that number less scary by spreading it out:
(1/32)^(-2/5)=(((1/32)^-1)^(1/5))^2
Now lets solve from the inside out.
=((32)^(1/5))^2
We can say this because: (1/32)^-1=32/1=32, and then we replace it within the equation. *Note: a '-1' exponent means to just flip the fraction or number*

=(2)^2

We can say this because 32^(1/5)=2 *Note: Unless you know logarithms, there's no way to know this other than using your calculator. Also, if the exponent is a fraction, it means to 'root' it e.g. 8^(1/3)=root3(2)*

=4

Last and easy step