exponents a^4/a^3=?

Answer 1

a

Answer 2

Rules for combining exponents in an expression: let a be the base and n and m be exponents, ok?

(a^m) * (a^n) = a^(m+n)

1/(a^n) = a^(-n)

so (a^m)/(a^n) = (a^m)*(a^-n) = a^(m-n)

Also, a^0 = 1 and a^1 = a

Back to your example, (a^4)/(a^3) = a(4-3) = a^1 = a

If this seems way too theoretical, get out pencil and paper, or your calculator and try it with a couple of numbers, like a=2 or a=3, just to satisfy yourself that it works.

Another way to think about it: a^4 = a*a*a*a
and a^3 = a*a*a

now take the ratio: a^4/a^3 = (a*a*a*a)/(a*a*a)

this is equal to a*[(a*a*a)/(a*a*a)] . The numerator and denominator of the expression inside the square brackets are the same, so they cancel out to 1.

Then a^4/a^3 = a*1 = a.

Answer 3

you pretty much just subtract the top exponents from the bottom ones.

a^(4-3) =a^1 =a

Answer 4

A^m/A^n = A^m-n
There fore A^4/a^3 = a^4-3 = a^1 = a

Answer 5

a^1 or just a

Answer 6

Come on, if you're studying this stuff then you learned that
a^m/a^n = a^(m-n)