How to simplify (−2x⁴)⁵ using exponent rules
Raise the coefficient and the variable power separately. The coefficient becomes (−2)⁵ = −32, and the power of x becomes (x⁴)⁵ = x²⁰. The result is −32x²⁰.
Keep the sign inside the parentheses
The fifth power multiplies five copies of −2. An odd number of negative factors leaves a negative product. With the same base and an even outer exponent, the coefficient would be positive.
Multiply the exponents
Each of the five factors supplies four copies of x, for twenty in total. This is why a power raised to a power multiplies the two exponents. When multiplying two separate powers of the same base, their exponents are added instead.
Check with a value
If x = 1, the original expression is (−2)⁵ and the simplified expression is −32. If x = 0, both expressions are zero. The checks can catch errors, while the product rule explains why the result holds for every real x.