Question

Simplify each expression.

$\left(-\mathbf{2}{u}^3\right)\left(\mathbf{5}u\right)$

Short answer

The expression $\left(-2u^3\right)\left(5u\right)$can be simplified as $-\mathbf{10}{u}^4$.

Step-by-step solution

Step 1. Group the coefficients and the variables.

Group the coefficients and variables in the given expression.

$\left(-2\right)\cdot \left(5\right)\left(u^3\cdot u\right)$

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.

$-\left(2\cdot 5\right)\left(u^{3+1}\right)$

Step 4. Simplify obtained expression.

Simplify the obtained expression in step 3.

$-10u^4$

Therefore, $\left(-2u^3\right)\left(5u\right)$can be simplified to $-10u^4$.