What is expand ((t^2)/p)^{1/3}(p/(t^5))^{1/2} ?

The solution to expand ((t^2)/p)^{1/3}(p/(t^5))^{1/2} is (p^{1/2}}{t^{5/2}}(\frac{t^2)/p)^{1/3}

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expand ((t^2)/p)^{1/3}(p/(t^5))^{1/2}

expand

(\frac{t ^{2}}{p})^{\frac{1}{3}} (\frac{p}{t ^{5}})^{\frac{1}{2}}

\frac{p ^{\frac{1}{2}}}{t ^{\frac{5}{2}}} (\frac{t ^{2}}{p})^{\frac{1}{3}}

Solution steps

(\frac{t ^{2}}{p})^{\frac{1}{3}} (\frac{p}{t ^{5}})^{\frac{1}{2}}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

\frac{p}{t ^{5}} = \frac{p ^{\frac{1}{2}}}{( t ^{5} ) ^{\frac{1}{2}}}

= \frac{p ^{\frac{1}{2}}}{( t ^{5} ) ^{\frac{1}{2}}} (\frac{t ^{2}}{p})^{\frac{1}{3}}

Simplify

(t^{5})^{\frac{1}{2}} : t^{\frac{5}{2}}

= (\frac{t ^{2}}{p})^{\frac{1}{3}} \frac{p ^{\frac{1}{2}}}{t ^{\frac{5}{2}}}

x^{2} (3 x - 4)^{2}

(2 x - 1)^{2} (2 x + 1)^{2}

2^{x - 3}

2 x^{2} (3 x^{3})

2 (23) (32)

What is expand ((t^2)/p)^{1/3}(p/(t^5))^{1/2} ?
The solution to expand ((t^2)/p)^{1/3}(p/(t^5))^{1/2} is (p^{1/2}}{t^{5/2}}(\frac{t^2)/p)^{1/3}