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Popular >

simplify 16^{4/3}

Solution

simplify

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

Solution

32 \cdot 2^{\frac{1}{3}}

+1

Solution steps

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

Prime factorization of

16 : 2^{4}

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

Apply exponent rule:

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

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

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

Apply exponent rule:

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

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

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

(2^{3})^{\frac{4}{3}} = 16

= 16 \cdot 2^{\frac{4}{3}}

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

= 16 \cdot 2 \cdot 2^{\frac{1}{3}}

Multiply the numbers:

16 \cdot 2 = 32

= 32 \cdot 2^{\frac{1}{3}}

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Frequently Asked Questions (FAQ)

What is 16^{4/3} ?
The solution to 16^{4/3} is 32*2^{1/3}