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

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Answer 1 · 2017-01-29T16:51:56

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

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#