Simplify the following: (x³x⁶)².

Add the exponents inside the parentheses to start, since they've got the same base.

(x³x⁶)² = (x⁹)²

Now multiply the 9 by 2, since one exponent is being raised to another.

(x⁹)² = x¹⁸

Simplify the following: (xy⁴)⁴y²z⁵.

Use the power rule, which tells you to multiply any exponent raised to another.

(xy⁴)⁴y²z⁵ = x⁴y¹⁶y²z⁵

Add the exponents of any like bases. In this case, this just means adding 16 to 2. You can do it.

x⁴y¹⁶y²z⁵ = x⁴y¹⁸z⁵

Simplify the following: (4a²b)³(-ab⁴).

First, we'll take care of the first set of parentheses using the power rule for our exponents. However, don't forget to treat the 4 out front like a regular old 4. This means that you need to cube 4 the way you would if it were 4³ all by itself.

(4a²b)³(-ab⁴) = 64a⁶b³(-ab⁴)

Next, get rid of the parentheses and multiply the coefficients. This means that the 64 gets multiplied by -1. Tough stuff.

64a⁶b³(-ab⁴) = -64a⁶b³ab⁴

Finish things up by adding exponents for factors whose bases are the same. Don't forget that a variable with no exponent implies the exponent is really 1: a = a¹.

-64a⁶b³ab⁴ = -64a⁷b⁷

Simplify the following: .

First things first. Anything to the power of 0 is just 1. So let's take care of that pesky y⁰ first.

(-5x(1)z²)³(¹⁄₅x³z⁵)² = (-5xz²)³(¹⁄₅x³z⁵)²

Now we'll take care of both sets of parentheses at the same time using the power rule. Once again, the -5 and are just numbers and need to be treated as such.

Finally, we can multiply the coefficients and the exponents where the bases are alike. This finishes things up nicely.