Question

Simplify each expression.

$\left(x^2\right)\left(\mathbf{7}{x}^8\right)$

Short answer

The expression$\left(x^2\right)\left(7x^8\right)$ can be simplified to $\mathbf{7}{x}^{10}$.

Step-by-step solution

Step 1. 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 2. Apply property of product of powers.

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

$7x^2\cdot x^8=7x^{2+8}$

Step 3. Simplify the expression.

Simplify the expression obtained in step 2.

$7x^{10}$

Therefore,$\left(x^2\right)\left(7x^8\right)$ can be simplified to $7x^{10}$.