Question

Simplify each expression.

$\left(-\mathbf{4}a{b}^4\right)\left(-\mathbf{5}{a}^5{b}^2\right)$

Short answer

The expression$\left(-4a{b}^4\right)\left(-5a^5{b}^2\right)$ can be simplified as $\mathbf{20}{a}^6{b}^6$.

Step-by-step solution

Step 1. Group the coefficients and the variables.

Group the coefficients and variables in the given expression.

$\left(-4\right)\cdot \left(-5\right)\left(a\cdot a^5\right)\left(b^4\cdot b^2\right)$

Step 2. Write the property of product of powers.

For any real number a and any integers m and n, $a^m\cdot a^n=a^{m+n}$.

Step 3. Apply property of product of powers.

Apply the property of product of powers to the expression obtained in step 1.

$\left(4\cdot 5\right)\left(a^{1+5}\right)\left(b^{4+2}\right)$

Step 4. Simplify obtained expression.

Simplify the obtained expression in step 3.

$20a^6{b}^6$

Therefore,$\left(-4a{b}^4\right)\left(-5a^5{b}^2\right)$ can be simplified to $20a^6{b}^6$.