simplify (1/8)^(-2/3) — step-by-step solution

Let's reduce:

{(\frac{1}{8})}^{- \frac{2}{3}}

ⓘ The factor is moved to the numerator or the denominator by changing the sign of its exponent, for a nonzero base:

{(\frac{1}{8})}^{- \frac{2}{3}}

\frac{1}{{(\frac{1}{8})}^{\frac{2}{3}}}

\frac{1}{{(\frac{1}{8})}^{\frac{2}{3}}}

ⓘ The power of a quotient is the quotient of the powers, (a/b)^n = a^n/b^n:

{(\frac{1}{8})}^{\frac{2}{3}}

\frac{1}{8^{\frac{2}{3}}}

\frac{1}{\frac{1}{8^{\frac{2}{3}}}}

ⓘ An exponent m/n means taking the nth root and then the mth power; here, the root of order

3

8

2

8^{\frac{2}{3}}

2^{2}

\frac{1}{\frac{1}{2^{2}}}

ⓘ Powers are computed before multiplications, additions and subtractions. An integer power is a repeated product:

2^{2}

2 \times 2

4

\frac{1}{\frac{1}{4}}

ⓘ Dividing is multiplying by the reciprocal:

\frac{1}{\frac{1}{4}}

4

▶Simplified form:

4