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Popular >

simplify sqrt(64^3)

Solution

simplify

6 4^{3}

Solution

512

Solution steps

6 4^{3}

Apply exponent rule:

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

6 4^{2 + 1} = 6 4^{2} \cdot 64

= 6 4^{2} \cdot 64

Apply radical rule:

ab = a b, a \geq 0, b \geq 0

6 4^{2} \cdot 64 = 6 4^{2} 64

= 6 4^{2} 64

Apply radical rule:

a^{2} = a, a \geq 0

6 4^{2} = 64

= 6464

Prime factorization of

64 : 2^{6}

= 64 2^{6}

Apply radical rule:

2^{6} = 2^{\frac{6}{2}}

= 64 \cdot 2^{\frac{6}{2}}

Divide the numbers:

\frac{6}{2} = 3

= 64 \cdot 2^{3}

2^{3} = 8

= 64 \cdot 8

Multiply the numbers:

64 \cdot 8 = 512

= 512

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Frequently Asked Questions (FAQ)

What is sqrt(64^3) ?
The solution to sqrt(64^3) is 512