Terms with Powers

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Terms with Powers

As with numeric powers, $a xx a = a^2$ , with the small 2 meaning that $a$ has been multiplied by itself.

Multiplying $a^2$ by $a$ is the same as $a xx a xx a$ , which is written as $a^3$ .

Like terms are multiplied together. $a^2b^2 x ab^2$ is the same as

$a xx a xx b xx b$ x $a xx b xx b$

= $a xx a xx a xx b xx b xx b xx b$

= $a^3b^4$

Example 1

Simplify $a xx a^2$

$a xx a^2 = a xx a xx a = a^3$

Answer: $a^3$

Multiply $ab^3$ by $a^2b$

$ab^3$ x $a^2b$

= $a xx b xx b xx b xx a xx a xx b$

= $a^3b^4$

Answer: $a^3b^4$