Question

Simplify each expression.

$\left(\mathbf{5}{a}^{7}b{c}^2\right)\left(-\mathbf{6}{a}^{2}b{c}^5\right)$

Short answer

The expression $\left(5a^{7}b{c}^2\right)\left(-6a^{2}b{c}^5\right)$can be simplified to $-\mathbf{30}{a}^9{b}^2{c}^7$.

Step-by-step solution

Step 1. Group the coefficients and the variables.

Group the coefficients and variables in the given expression.

$\left(5\right)\cdot \left(-6\right)\left(a^7\cdot a^2\right)\left(b\cdot b\right)\left(c^2\cdot c^5\right)$

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 in step 1.

$-\left(5\cdot 6\right)\left(a^{7+2}\right)\left(b^{1+1}\right)\left(c^{2+5}\right)$

Step 4. Simplify obtained expression.

Simplify the obtained expression in step 3.

$-30a^9{b}^2{c}^7$

Therefore, $\left(5a^{7}b{c}^2\right)\left(-6a^{2}b{c}^5\right)$can be simplified to $-30a^9{b}^2{c}^7$.