If a ≠ 0 , then what does a^9/a^5 equal?

Question

the title says it, i dont understand what the question even means

If  then what does a⁹/a⁵ equal?

Answer 1

The quotient rule states that when dividing two powers that have the same base, subtract their exponents.

Since each of the powers in this problem has a base of a,

we can simplify the expression by subtracting the exponents.

9 - 5 is 4 so our answer is a⁴.

Answer 2

a⁹/a⁵ = a^9-5 = a⁴

Note that the above statement is only valid when "a" is not "zero".

When "a" is "zero", this operation will result in "nothing": division by "0", simply, does not exist.

We cannot divide a cake by zero people, right?

That is why division by "zero" in mathematics is "undefined".

Answer 3

The Question: The question is asking for you to simplify the equation, but first stating that the variable is not equal to 0 (because dividing by 0 gives an undefined answer). We can simplify the expression even though we do not know what number the variable is.

The Answer: We keep the variable the same and subtract the exponent in the numerator from the exponent in the denominator. This is called the Quotient Rule. We subtract 5 from 9 to get a⁴.

The Proof: The exponent is how many times the variable is multiplied by itself, so the equation can be written out with 9 of the varible on the top and 5 on the bottom:

a a a a a a a a a / a a a a a

You can then cancel out one varible from the numerator for each from the denominator (since any number divided by itself is 1):

a a a a a a a a a / a a a a a

This gives us 4 of the varible in the numerator, which can be written as a⁴

Answer 4

The a≠0 part just means don't worry about dividing by zero.

This is just an exponent exercise:

a⁹/a⁵ = a⁹a^-5 = a^9-5 = a⁴

And that's it.

Answer 5

The statement a≠0 is there because if a did equal 0 there would be division by 0 which is undefined.

So a⁹ / a⁵, by the 2nd Law of Exponents is a⁴ (based on a^(9-5).