Mathematics
OpenStudy (anonymous):

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

OpenStudy (anonymous):

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: $m^5 \over 8x^2q^5$

OpenStudy (anonymous):

Lovely explanation, but YOU did all the work.