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simplifying numbers

How would I simplify 2^-3 X 2 (2 to the negative 3rd power times 2) ? I know that it has to be like 4, or maybe 1/4...

Also, how would I simplify x^30 / x^-10? I know that it is roughly x^40 but I'm not exactly sure.

$2^{-3} \times 2 = 2^{-3} \times 2^1$

When two numbers, having same base are multiplied, add their powers.

$2^{-3} \times 2^1 = 2^{-3+1} = 2^{-2}$

When two numbers, having same base, one is divided by the other, subtract their powers.

$\frac{x^30}{x^-10} = x^{30--10} = x^{30+10} = x^{40}$

Hope that helped!

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