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Popular >

simplify (9p^{2/3})^{5/2}

Solution

simplify

(9 p^{\frac{2}{3}})^{\frac{5}{2}}

Solution

243 p^{\frac{5}{3}}

Solution steps

(9 p^{\frac{2}{3}})^{\frac{5}{2}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(9 p^{\frac{2}{3}})^{\frac{5}{2}} = 9^{\frac{5}{2}} (p^{\frac{2}{3}})^{\frac{5}{2}}

= 9^{\frac{5}{2}} (p^{\frac{2}{3}})^{\frac{5}{2}}

9^{\frac{5}{2}} = 243

= 243 (p^{\frac{2}{3}})^{\frac{5}{2}}

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

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

= 243 p^{\frac{2}{3} \cdot \frac{5}{2}}

Cross-cancel:

2

= 243 p^{\frac{5}{3}}

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Frequently Asked Questions (FAQ)

What is (9p^{2/3})^{5/2} ?
The solution to (9p^{2/3})^{5/2} is 243p^{5/3}