 Further expressions involving division law with variable bases

Lesson

We've learnt about the division law which states:

$\frac{a^x}{a^y}=a^{x-y}$axay=axy

Now we are going to apply this rule to questions that also have integer coefficients and more than one unknown value. We are also going to look at expressions that involve the power law. It's the same principle - just remember you can only apply the division rule to terms with like bases (and, of course, we can simplify numeric expressions as normal).

Examples

Question 1

Simplify the following, giving your answer in positive or negative exponential form:

$\frac{-9x^{13}}{3x^4}$9x133x4

Question 2

$\frac{5^{2x}}{5^{x+1}}$52x5x+1

Question 3

Convert the following to a fraction and simplify using the exponent laws:

$\left(-240u^{32}\right)\div\left(-8u^9\right)\div\left(-5u^{12}\right)$(240u32)÷​(8u9)÷​(5u12)

Outcomes

9D.NA1.04

Extend the multiplication rule to derive and understand the power of a power rule, and apply it to simplify expressions involving one and two variables with positive exponents