Further expressions involving division law with variable bases
We've learnt about the division law which states:
$\frac{a^x}{a^y}=a^{x-y}$axay=ax−y
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)