How do I simplify this exponent?

Question

I'm having trouble simplifying these kinds of exponents:

4^n/(3^(n-1))

Can anyone help me step by step?

Answer 1

split it up

4^n * 1 / (3^(n-1)

4^n is good...don't mess around with that

For get for now that 3^(n-1) is in the denominator.

Since we are simplfying...we know we want to do something with the number and get 3^n

What we'd do is make it

3^n / 3. Remember 3 = 3^1.
If you remember your rules......for instance. X^5 / X^3 = X^(5-3)
so when we divide we subtract the exponents.
3^n / 3 = 3^(n-1).....thats how we got the number
3^n/3

Since that number was originall in the denominator....just take the reciprocal.
3/3^n.

Now put your equaiton back together
4^n * 3/3^n.

Now remember your other rules about multiply / dividing numbers with teh same exponent......example
2^3 / 3^3 = (2/3)^3

so we get
3(4/3)^n
*****my tips on how to remember, but they might confuse you more...you can ingore this part*******
I sometimes get confused with the rules...so the easiest way to remember is to sub in numbers and use an easy case.

So the exponent rule

Just use 2^4 and 2^2...both numbers you should know.....16 and 4

anyways.
2^4 / 2^2.......if you ahve trouble remmebering what to do...just do 16/4 = 4. so we know our answer is 2^2....we must've subtracted our exponents.

THen use the number 3 and 2

3^3 and 2^3.
3^3 / 2^3......can't remember what to do. 27/8
So probalby have to use a calculator....but plug in all the different variations you konw. Do we subtract exponents..do we add...etc

you finally get (3/2)^3.

Answer 2

bear in mind that when you divide effortless bases, you SUBTRACT the exponents: -5 - (-2) -5 + 2 Exponent: -3 y^-3 --> Rewrite as a favorable exponent. answer: a million / y^3 wish that facilitates.

Answer 3

4^(n) / [ 3^(n) x 3^(-1)]
= [4^(n) / 3^(n)] x 3
= (4/3)^n x 3

Answer 4

x^(a+b) = x^a * x^b

4^n / 3^(n-1) = 4 * 4^(n-1) / 3^(n-1) = 4 (4/3)^(n-1)
or equally good is 3(4/3)^n