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Popular >

simplify \sqrt[4]{64^3}

Solution

simplify

4 6 4^{3}

Solution

162

+1

Decimal

22.62741 \dots

Solution steps

4 6 4^{3}

Apply radical rule:

n a = a^{\frac{1}{n}}

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

Apply exponent rule:

(a^{b})^{c} = a^{b c}

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

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

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

6 4^{\frac{3}{4}} = (244)^{3}

= (244)^{3}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

= 2^{3} (44)^{3}

(44)^{3} : 4^{\frac{3}{4}}

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

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

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

2^{\frac{3}{2}} = 22

= 2^{3} \cdot 22

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

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

= 2^{3 + 1} 2

Add the numbers:

3 + 1 = 4

= 2^{4} 2

2^{4} = 16

= 162

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Frequently Asked Questions (FAQ)

What is \sqrt[4]{64^3} ?
The solution to \sqrt[4]{64^3} is 16sqrt(2)