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Popular >

simplify sqrt(16^3)

Solution

simplify

1 6^{3}

Solution

64

Solution steps

1 6^{3}

Apply exponent rule:

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

1 6^{2 + 1} = 1 6^{2} \cdot 16

= 1 6^{2} \cdot 16

Apply radical rule:

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

1 6^{2} \cdot 16 = 1 6^{2} 16

= 1 6^{2} 16

Apply radical rule:

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

1 6^{2} = 16

= 1616

Prime factorization of

16 : 2^{4}

= 16 2^{4}

Apply radical rule:

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

= 16 \cdot 2^{\frac{4}{2}}

Divide the numbers:

\frac{4}{2} = 2

= 16 \cdot 2^{2}

2^{2} = 4

= 16 \cdot 4

Multiply the numbers:

16 \cdot 4 = 64

= 64

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Frequently Asked Questions (FAQ)

What is sqrt(16^3) ?
The solution to sqrt(16^3) is 64