In Multiplying Multiple Powers, we looked at the multiplication law, which states:
$a^x\times a^y=a^{x+y}$ax×ay=ax+y
The base terms needs to be the same to apply this rule.
We can also apply the multiplication rule to terms with negative exponents. We just need to remember how to add with negative numbers.
Also, we may be asked to express terms with negative exponents with positive exponents instead. To do this, we need to apply the negative exponent rule, which states:
$a^{-x}=\frac{1}{a^x}$a−x=1ax
Let's look through some examples now to see these processes in action.
Examples
Question 1
Rewrite $10^{-10}\times10^4$10−10×104 in the form $a^n$an.
Question 2
Simplify the following, giving your answer with a positive exponent: $p^2\times p^{-7}$p2×p−7
Question 3
Simplify the following, writing without negative exponents.
$2p^5q^{-7}\times6p^{-9}q^9$2p5q−7×6p−9q9