New Zealand
Level 6 - NCEA Level 1

# 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 index 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 index laws:

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

### Outcomes

#### NA6-2

Extend powers to include integers and fractions.

#### 91026

Apply numeric reasoning in solving problems