Powers & Percentage Increase/Decrease

Hi, I'm revising for my gcse exam in June and struggling with these two topics.

Percentage Decrease: What is the new cost after a price of £56 is decreased by 15%? Work it out as 0.85 5g=£47.50 This is a question from a GCSE revision guide, I don't really get this. I have tried to find a way to understand but I really don't- I don't understand where the 0.85 came from. Multiplying powers- again this is a question from a rev guide- 48=32, but 48=2₂ 2₃=2₅ =32 I don't understand how 2 to the power of 3 is 8,

Percentage Decrease: Question from GCSE - 243 / 9 =7, but 243 / 9 = 3₅ / 3₂ = 3₃= 27

Can you please explain all these questions to me, sorry that I'm asking to many questions but please can you answer them, this is the only thing I'm struggling on. Thank You 😀

Answers
The last question is diving powers, sorry
addycole_786
11 April 2012
If £56 is decreased by 15%, then it means that 15% of £56 is subtracted. Another way of looking at it is to say that you have 85% of it left. 85% is just another way of expressing the fraction 0.85 . To find out how much is 0.85 of £56 you just multiply the numbers together. The word "of" can almost always be replaced with a multiplication sign.
ianmoth
11 April 2012
Apparently 243 is 3 x 3 x 3 x 3 x 3 , ie, 3^5. 9 is 3 x 3 , or 3^2. So if you have a fraction where you have 3^5 on the top line and 3^2 on the bottom line, then you can cancel out two of the threes, to leave 3^3 on its own. This is the same as subtracting the power on the bottom line from the power on the top, ie, 5-2=3. 3^3 = 3 x 3 x 3 = 27
ianmoth
11 April 2012
Thank You, I understand it now :D
addycole_786
12 April 2012
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