⚠ (-128)^{5/7} is read as (-128)^(5/7): use ^(...) to group an exponent, use * to multiply

Let's reduce: ${\left(-128\right)}^{\frac{5}{7}}$

ⓘ 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: ${\left(-128\right)}^{\frac{5}{7}}$ = $-{128}^{\frac{5}{7}}$

$-{128}^{\frac{5}{7}}$

ⓘ Without parentheses, the minus sign is not part of the power■An exponent m/n means taking the nth root and then the mth power; here, the root of order $7$ of $128$ is $2$: $-{128}^{\frac{5}{7}}$ = $-2^5$

$-2^5$

ⓘ Without parentheses, the minus sign is not part of the power■An integer power is a repeated product: $-2^5$ = $-(2\times \mathrm{...}\times 2)$, 5 times = $-32$

▶Simplified form:   $-32$