Chapter 11, Problem 1RE

To determine

To simplify: The expression $x^5\cdot x^5$ and write the answer with positive exponent.

Answer to Problem 1RE

The expression $x^5\cdot x^5$ can be simplified as $\underset{\_}{x^5\cdot x^5=x^{10}}$.

Explanation of Solution

Rule used:

To multiply powers that have like bases:

1. Verify that the bases are the same. Use this base as the base of the product.

2. Add the exponent for the exponent of the product.

The rule can be stated symbolically as $a^m\cdot a^n=a^{m+n}$ where $a,m$ and n are real numbers and $a\ne 0$.

Calculation:

The given expression is $x^5\cdot x^5$.

It is to be noted from the expression that the bases are same. So, add the exponent and simplify the expression $x^5\cdot x^5$ as follows:

$\begin{array}{c}{x}^5\cdot x^5=x^{5+5}\left[\because a^m\cdot a^n=a^{m+n}\right]\\ =x^{10}\end{array}$

Therefore, the expression $x^5\cdot x^5$ can be simplified as $\underset{\_}{x^5\cdot x^5=x^{10}}$.