Q11. - Algebra 1

Question

Simplify each expression.

$\mathit{x}\mathbf{\cdot }{\mathit{x}}^3\mathbf{\cdot }{\mathit{x}}^5$

Step-by-Step Solution

Answer

The expression $x\cdot x^3\cdot x^5$ can be simplified as ${\mathit{x}}^9$.

Step 1. Write the property of product of powers.

For any real number 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 given expression.

$x\cdot x^3\cdot x^5=x^{1+3+5}$

Step 3. Simplify obtained expression.

Simplify the obtained expression in step 2.

$x^9$

Therefore, $x\cdot x^3\cdot x^5$ can be simplified to $x^9$.