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Popular >

simplify (9^{1/2})^3

Solution

simplify

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

Solution

27

Solution steps

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

Apply exponent rule:

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

= 9^{\frac{1}{2} \cdot 3}

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

= 9^{\frac{3}{2}}

Factor the number:

9 = 3^{2}

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

Apply exponent rule:

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

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

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

= 3^{3}

3^{3} = 27

= 27

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Frequently Asked Questions (FAQ)

What is (9^{1/2})^3 ?
The solution to (9^{1/2})^3 is 27