Q&A for How to Divide Exponents

It would be the fraction (a/b) raised to the power of c.

First of all, the two positive numbers (the bases) have to be the same. If they are, you subtract the exponent in the denominator from the exponent in the numerator. If the denominator's exponent is negative, you treat it as if it were positive and add it to the numerator's exponent. Thus, x^3 ÷ x^(-1) = x^4.

400 / 10³ = 400 / 1000 = 0.4.

Any whole number (except zero) will divide into any other whole number, although in many cases you'll wind up with a remainder. However, if you're talking about exponential expressions, the base number in the numerator must match the base number in the denominator, in which case you simply subtract the denominator's exponent from the numerator's exponent and retain the base number.

(4/3)ˆ4 / (2/9)ˆ4 = [ (4/3)/(2/9) ]ˆ4 ...[aˆn / bˆn = (a/b)ˆn] = [ (4/3) x (9/2) ]ˆ 4 = [ (4x9)/(3x2) ]ˆ4 = [ 36/6 ]ˆ4 = [ 6 ]ˆ4 = 1296

Let's assume you are trying to divide (x + y) by [(x^-1) + (y^-1)]. The denominator (the expression in brackets) can be simplified this way: [(x^-1) + (y^-1)] = (1/x) + (1/y) = (y/xy) + (x/xy) = (y + x) / xy = (x + y) / xy. Taking this last expression as the new denominator, we now have (x + y) / [(x + y) / xy]. Because the denominator is now a fraction, we can invert it and multiply by the numerator to get the final result. Thus, (x + y)(xy / (x + y) = xy. The final answer is xy. If this is confusing, remember that to divide by a fraction, you invert the fraction and multiply it by the other number.

Yes. (8/9)² = 8² / 9² = 64 / 81.

First evaluate each base-and-exponent pair, then do the division. For example, 2^8 / 3³ = 256 / 27 = 9.48.

(2^6)(5^5) = (64)(3125) = 200,000.

(-2)² / 3 = 4 / 3.

Any number divided by itself equals 1.

6 x 6 x 6 = 216. 3 x 3 x 3 x 3 = 81. Divide 216 by 81.

[a^m]^(1/n). This means the nth root of (a^m).

Subtract the exponent. y^2/y^3 = y^(2-3) = y^(-1) = 1/y Whenever a number has a negative exponent, you have to invert it to get a positive exponent. Like y^(-1) = 1/y^1 = 1/y.

You cannot divide them, because they do not have the same base (a and b). So you have to leave the expression as (a^x) / (b^y).

This is a polynomial divided by a polynomial. See Divide Polynomials and Divide Polynomials Using Synthetic Division

(5 x 10^9) ÷ (1 x 10^10) = (5/1) x 10^(9 - 10) = 5 x 10^(-1) = 5 x (0.1) = 0.5 = 1/2.

x² / x³ = x^(2 - 3) = x^(-1) = 1 / x^(1) = 1 / x.

If you mean that the exponent in the denominator is larger than the exponent in the numerator (and the bases are the same), yes, you will wind up with a negative exponent in the answer. A negative exponent indicates a reciprocal. Thus, for example, x^ 6 / x^8 = x^(-2) = 1/x².