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Popular >

simplify (9^{5/3})^{3/10}

Solution

simplify

(9^{\frac{5}{3}})^{\frac{3}{10}}

Solution

3

Solution steps

(9^{\frac{5}{3}})^{\frac{3}{10}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

= 9^{\frac{5}{3} \cdot \frac{3}{10}}

\frac{5}{3} \cdot \frac{3}{10} = \frac{1}{2}

= 9^{\frac{1}{2}}

Factor the number:

9 = 3^{2}

= (3^{2})^{\frac{1}{2}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

= 3^{2 \cdot \frac{1}{2}}

2 \cdot \frac{1}{2} = 1

= 3^{1}

Apply exponent rule:

a^{1} = a

= 3

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Frequently Asked Questions (FAQ)

What is (9^{5/3})^{3/10} ?
The solution to (9^{5/3})^{3/10} is 3