Let's simplify: ${\left(-2x^4\right)}^5$

ⓘ With an even integer exponent, the minus sign in the base disappears; with an odd integer exponent, it moves in front of the power: ${(-2x^4)}^5$ = $-{\left(2x^4\right)}^5$

$-{\left(2x^4\right)}^5$

ⓘ The power of a product is the product of the powers: $-{\left(2x^4\right)}^5$ = $-2^5·{\left(x^4\right)}^5$

$-2^5·{\left(x^4\right)}^5$

ⓘ Powers are computed before multiplications, additions and subtractions. An integer power is a repeated product: $2^5$ = $2·\mathrm{...}·2$, 5 times = $32$■A power of a power multiplies the exponents, (a^n)^m = a^(n*m): ${\left(x^4\right)}^5$ = $x^{4·5}$

$-32x^{4·5}$

ⅰ $4·5$ = $20$

▶Simplified form:   $-32x^{20}$