I've just come across a grade A question involving indices: $$\frac{2^{30}}{8^9} = 2^x$$ Work out the value of $x$. As a tip, the revision guide says to convert $8^9$ to $2^{something}$ so the question can be simplified by subtracting the indices. But I have no idea how to do this and I can't find anything on it.


2 Answers 2


$$8 = 2^3$$ $$8^9 = (2^3)^9$$

When we raise an exponent to another exponent, we multiply them together:

$$8^9 = (2^3)^9 = 2^{(3*9)} = 2^{27}$$

So now your problem becomes:

$$\frac{2^{30}}{2^{27}} = 2^{(30-27)} = 2^3 = 8$$

  • 2
    $\begingroup$ I'd just like to thank you for taking the time to answer this. I know it might've been simple but with a math teacher that never has the time to answer my questions and all my revision books not having anything on this it really means a lot to finally find out how to do this. I really appreciate your help! $\endgroup$
    – Eva
    Apr 5, 2016 at 18:37
  • $\begingroup$ Mhm, not a problem! That's what these websites are for, right? If you need any other help don't feel hesitant to post - the community is extremely helpful and has given me a lot of intuition on questions I had previously, even if I thought they might have been simple or trivial. (: $\endgroup$
    – anonymouse
    Apr 5, 2016 at 18:42

Notice that $8$ can be written as $2^3$. See if this helps you continue with the equation.


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