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Popular >

simplify (8)^{2/3}(16)^{1/4}

Solution

simplify

(8)^{\frac{2}{3}} (16)^{\frac{1}{4}}

Solution

8

Solution steps

8^{\frac{2}{3}} \cdot 1 6^{\frac{1}{4}}

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

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

Factor the number:

16 = 2^{4}

= 4 (2^{4})^{\frac{1}{4}}

Apply exponent rule:

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

(2^{4})^{\frac{1}{4}} = 2^{4 \cdot \frac{1}{4}}

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

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

= 4 \cdot 2^{1}

Apply exponent rule:

a^{1} = a

2^{1} = 2

= 4 \cdot 2

Multiply the numbers:

4 \cdot 2 = 8

= 8

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Frequently Asked Questions (FAQ)

What is (8)^{2/3}(16)^{1/4} ?
The solution to (8)^{2/3}(16)^{1/4} is 8