Question

How do you simplify `(2xy^6)^5`?

Answer 1

The answer will be `32x^5y^30`. Explanation follows...

Explanation:

When you make a power in which the base is another power, the simplifying involves multiplying the exponents. For example

`(x^3)^4= x^(3*4)=x^12`

Here's why:

`x^3 = x*x*x`

so, `(x^3)^4=(x*x*x)*(x*x*x)*(x*x*x)*(x*x*x)`

which, as you can see is nothing more than twelve `x`'s all multiplied in one product, and that can be written `x^12`.

Don't forget that is you see no exponent on a base, you are to imagine a `1` there.

So `(2xy^6)^5=2^5*x^5*(y^6)^5=32x^5y^30`