I am having trouble with exponents, can anyone help? (2m^2q^-1)^3(mx)^-1 -------------------- (8qx^1/2)^2

So, you have \[(2m^2q^{-1})^3(mx)^{-1} \over (8qx^{1/2})^2\] We have to simplify this. When you have exponent in the form \[(a^n)^m\] you can rewrite this as \[a^{nm}\] (and vice versa of course). This gives us simpler expression: \[(8m^6q^{-3})(mx)^{-1} \over x(8q)^2\] We can simplify better because we have negative exponents. Negative exponents have the following property: \[a^{-n} = {1 \over a^n}\] Now, move negative exponents from numerator to denominator: \[8m^6 \over mq^3x^2(8q)^2\] So, we got rid off negative exponents. Now, notice that we have \[m\] in numerator and denominator, \[{a^n over a^m} = a^{n-m}\] So, we get: \[8m^5 \over q^3x^2(8q)^2\] You've probably noticed that we have here untouched \[(8q)^2\] We have to use this property now: \[a^n * a^m = a^{n+m}\] and this gives us: \[8m^5 \over 64x^2q^5\] Now, divide by 8: \[m^5 \over 8x^2q^5\]

Lovely explanation, but YOU did all the work.

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