When multiplying factors which contains variables, we multiply the coefficient and a variables as usual. In the variable, if the bases are the same, we can multiply the base by adding their exponents.

**Example:** $a^{3} \times a^{2} \times b^{4} \times b^{3}$

$a^{3} \times a^{2}$ =
$a^{3 + 2}$

$b^{4} \times b^{3}$ = $b^{4 + 3}$

$a^{3} \times a^{2} \times b^{4} \times b^{3}$ =
$a^{3 + 2} \times
b^{4 + 3}$

=
$a^{5} b^{7}$

### Examples on Multiplying Variables with Exponents

Given below are some examples on multiplying variables with exponents

**Example 1:** $4 \times p^{3}
\times p^{4}
\times 2 \times q^{1} \times q^{2} \times 3
\times r^{5}$

**Solution:**

Given ^{}$4 \times p^{3} \times p^{4} \times 2 \times q^{1} \times q^{2} \times 3 \times r^{5}$

Multiplying bases and adding exponents,

$p^{3} \times p^{4}$ = $p^{3 + 4}$

$q^{1} \times q^{2}$ = $q^{1 + 2}$
^{}

$r^{5}$ = ^{}$r^{5}$

$4 \times 2 \times 3$ = $24$

Combine the terms

$4 \times p^{3} \times p^{4} \times 2 \times q^{1} \times q^{2} \times 3 \times r^{5}$ = $4 \times 2 \times 3 \times p^{3 + 4} \times q^{1 + 2} \times r^{5}$

= $24 \times p^{7} \times q^{3} \times r^{5}$

**Example 2:**

$2 \times a^{2} \times a^{6} \times b^{7} \times b^{3} \times 5 \times c^{9}$^{}

**Solution:**

Given
$2 \times a^{2} \times a^{6} \times b^{7} \times b^{3} \times 5 \times c^{9}$

Multiplying bases and adding exponents

$a^{2} \times a^{6}$ = $a^{2 + 6}$

$b^{7} \times b^{3}$ = $b^{7 + 3}$

$c^{9}$ = $c^{9}$

$2 \times 5$ = $10$

Combine the terms

= $(2 \times 5) \times a^{2 + 6} \times b^{7 + 3} \times c^{9}$

= $10 \times a^{8} \times b^{10} \times c^{9}$

^{}