Simplify (-5z^2)^3(4z^3)

Problem

(−5*z2)3*(4*z3)

Solution

1. Apply the power of a product rule to the first term (−5*z2)3 by raising both the coefficient and the variable to the third power.

(−5*z2)3=(−5)3⋅(z2)3

2. Evaluate the exponent for the constant and apply the power of a power rule (am)n=a(m*n) to the variable.

(−5)3=−125

(z2)3=z(2⋅3)=z6

3. Substitute the simplified term back into the original expression.

−125*z6⋅4*z3

4. Multiply the coefficients and apply the product rule for exponents am⋅an=a(m+n) to the variables.

−125⋅4=−500

z6⋅z3=z(6+3)=z9

Final Answer

(−5*z2)3*(4*z3)=−500*z9

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