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Popular >

simplify 24^{(-2)/3}

Solution

simplify

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

Solution

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

+1

Decimal Notation

0.12018 \dots

Solution steps

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

Prime factorization of

24 : 2^{3} \cdot 3

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

Apply exponent rule:

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

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

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

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

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

Apply the fraction rule:

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

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

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

Apply exponent rule:

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

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

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

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

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

Popular Examples

∣ a - 5 ∣ = 5 - a

(x^2)/2-(3x)/(20)= 1/5

\frac{x ^{2}}{2} - \frac{3 x}{20} = \frac{1}{5}

∣ 5 x + 1 ∣ = ∣ 8 x + 4 ∣

factor 3x^2-12x-9 factor

3 x^{2} - 12 x - 9

∣ x - 4 ∣ < 1

Frequently Asked Questions (FAQ)

What is 24^{(-2)/3} ?
The solution to 24^{(-2)/3} is 1/(4*3^{2/3)}