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Popular >

simplify 16^{(-2)/3}

Solution

simplify

1 6^{\frac{- 2}{3}}

Solution

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

+1

Solution steps

1 6^{\frac{- 2}{3}}

Prime factorization of

16 : 2^{4}

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

Apply exponent rule:

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

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

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

Apply exponent rule:

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

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

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

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

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

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

\frac{- 2}{3} = - \frac{2}{3}

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

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

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

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

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

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

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Frequently Asked Questions (FAQ)

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