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Popular >

simplify (16^{3/2})^{1/2}

Solution

simplify

(1 6^{\frac{3}{2}})^{\frac{1}{2}}

Solution

8

Solution steps

(1 6^{\frac{3}{2}})^{\frac{1}{2}}

Apply exponent rule:

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

= 1 6^{\frac{3}{2} \cdot \frac{1}{2}}

\frac{3}{2} \cdot \frac{1}{2} = \frac{3}{4}

= 1 6^{\frac{3}{4}}

Factor the number:

16 = 2^{4}

= (2^{4})^{\frac{3}{4}}

Apply exponent rule:

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

= 2^{4 \cdot \frac{3}{4}}

4 \cdot \frac{3}{4} = 3

= 2^{3}

2^{3} = 8

= 8

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Frequently Asked Questions (FAQ)

What is (16^{3/2})^{1/2} ?
The solution to (16^{3/2})^{1/2} is 8