Question

Match the expression to the exponent property that you use first to simplify the expression.

Answer 1

Step-by-step explanation:

$\dfrac{a^m}{a^n}=a^{m-n}\to\dfrac{h^\frac{3}{2}}{h^\frac{4}{3}}=h^{\frac{3}{2}-\frac{4}{3}}=h^{\frac{(3)(3)}{(2)(3)}-\frac{(2)(4)}{(2)(3)}}=h^{\frac{9}{6}-\frac{8}{6}}=h^{\frac{1}{6}}\\\\(a^m)^n=a^{mn}\to\bigg(p^\frac{1}{4}\bigg)^\frac{2}{3}=p^{\left(\frac{1}{4}\right)\left(\frac{2}{3}\right)}=p^\frac{2}{12}=p^\frac{1}{6}\\\\a^m\cdot a^n=a^{m+n}\to z^\frac{3}{4}\times z^\frac{5}{6}=z^{\frac{3}{4}+\frac{5}{6}}=z^{\frac{(3)(3)}{(4)(3)}+\frac{(5)(2)}{(6)(2)}}=z^{\frac{9}{12}+\frac{10}{12}}=z^\frac{19}{12}$

$\left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\to\bigg(\dfrac{x^2}{y}\bigg)^\frac{1}{3}=\dfrac{\left(x^2\right)^\frac{1}{3}}{y^\frac{1}{3}}=\dfrac{x^{(2)\left(\frac{1}{3}\right)}}{y^\frac{1}{3}}=\dfrac{x^\frac{2}{3}}{y^\frac{1}{3}}$