NZ Level 6 (NZC) Level 1 (NCEA)
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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

Simplify the following, giving your answer in index form:

$\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

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