Chapter 4.3, Problem 4OE

To determine

To Simplify: The expression $c\cdot c^6\cdot c^3$

Answer to Problem 4OE

The required answer is $c^{10}$ .

Explanation of Solution

Given information:

The expression $c\cdot c^6\cdot c^3$

Concept Used:

An exponent represents the number of times the base is used as a factor.

For Example:

  $a^3=a\cdot a\cdot a$

Rule of exponents for product of powers states that to multiply two powers with same base, the exponents are added.

For example $a^m\cdot a^n=a^{m+n}$

Calculation:

  $c\cdot c^6\cdot c^3$

Using rule of exponents for product of powers

  $\begin{array}{l}=c^{1+6}\cdot c^3\\ =c^7\cdot c^3\\ =c^{10}\end{array}$