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Popular >

simplify 8^{1/3}*64^{1/3}

Solution

simplify

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

Solution

8

Solution steps

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

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

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

Factor the number:

64 = 4^{3}

= 2 (4^{3})^{\frac{1}{3}}

Apply exponent rule:

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

(4^{3})^{\frac{1}{3}} = 4^{3 \cdot \frac{1}{3}}

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

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

= 2 \cdot 4^{1}

Apply exponent rule:

a^{1} = a

4^{1} = 4

= 2 \cdot 4

Multiply the numbers:

2 \cdot 4 = 8

= 8

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Frequently Asked Questions (FAQ)

What is 8^{1/3}*64^{1/3} ?
The solution to 8^{1/3}*64^{1/3} is 8