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

Jan 29, 2017

The answer will be $32 {x}^{5} {y}^{30}$. Explanation follows...

#### Explanation:

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

${\left({x}^{3}\right)}^{4} = {x}^{3 \cdot 4} = {x}^{12}$

Here's why:

${x}^{3} = x \cdot x \cdot x$

so, ${\left({x}^{3}\right)}^{4} = \left(x \cdot x \cdot x\right) \cdot \left(x \cdot x \cdot x\right) \cdot \left(x \cdot x \cdot x\right) \cdot \left(x \cdot x \cdot x\right)$

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 ${\left(2 x {y}^{6}\right)}^{5} = {2}^{5} \cdot {x}^{5} \cdot {\left({y}^{6}\right)}^{5} = 32 {x}^{5} {y}^{30}$