Help with rules of exponents

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Mortzy

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Dec 16, 2019
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( I don't know how to put in exponents so I used ^ to represent it) I was given an equation ((2^2)^w)^3=(2^5)^(w-1) and using exponent rules I am supposed to get 2^(6w)=2^(5w-5).
I can't figure out how they did it and what rules I should learn or techniques to study to make that simplification. Thank you!
 
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Mortzy said:
( I don't know how to put in exponents so I used ^ to represent it) I was given an equation ((2^2)^w)^3=(2^5)^(w-1) and using exponent rules I am supposed to get 2^(6w)=2^(5w-5).
I can't figure out how they did it and what rules I should learn or techniques to study to make that simplification. Thank you!
Click to expand...
You need to use:

\(\displaystyle (a^b)^c = a^{(b * c)}\)...................................... We use '*' to signify multiplication"

Notice that I corrected your original post and inserted parentheses (). Those are very important to show order of operations.
 
Consider (3^2)^3. Now just use definitions! (3^2)^3 means (3^2)*(3^2)*(3^2) which means (3*3)*(3*3)*(3*3) which means (3*3*3*3*3*3) which means 3^6. Look carefully at what I wrote and see for yourself how the power came to be 6. If you don't see why, then try a few more similar ones. You have to see it yourself, us telling you will what to do with the powers will not help very much.
 
Mortzy said:
( I don't know how to put in exponents so I used ^ to represent it) I was given an equation ((2^2)^w)^3=(2^5)^(w-1) and using exponent rules I am supposed to get 2^(6w)=2^(5w-5).
I can't figure out how they did it and what rules I should learn or techniques to study to make that simplification. Thank you!
Click to expand...
The first three powers are 2, w and 3. How do you get 6w from them? The next two powers are 5 and (w-1). How do you get 5w-5 from them?
 
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