Let's evaluate: ${\left({\left(-8\right)}^{\frac{2}{3}}\right)}^{\frac{3}{2}}$

ⓘ For a reduced rational exponent m/n with odd n, use the real root: the result is negative for odd m and positive for even m: ${\left(-8\right)}^{\frac{2}{3}}$ = $8^{\frac{2}{3}}$■For a real base and a reduced exponent with even numerator and odd denominator, take the absolute value of the base before multiplying the exponents: ${\left(8^{\frac{2}{3}}\right)}^{\frac{3}{2}}$ = ${\left|8\right|}^{\frac{2}{3}\times \frac{3}{2}}$

${\left|8\right|}^{\frac{2}{3}\times \frac{3}{2}}$

ⓘ To multiply fractions, multiply the numerators together and the denominators together: $\frac{2}{3}\times \frac{3}{2}$ = $\frac{2\times 3}{3\times 2}$ = $\frac{6}{6}$

${\left|8\right|}^{\frac{6}{6}}$

ⓘ We simplify the fraction by dividing the numerator and the denominator by $6$, their greatest common divisor: $\frac{6}{6}$ = $1$

${\left|8\right|}^1$

$\left|8\right|$

ⓘ The expression inside the absolute value is nonnegative, so its absolute value equals that expression: $\left|8\right|$ = $8$

▶Result:   $8$