Q&A for How to Divide Exponents

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  • Question
    How can I divide a by b, if both have exponent c?
    Donagan
    Top Answerer
    It would be the fraction (a/b) raised to the power of c.
  • Question
    How do I divide a positive number with a positive exponent by a positive number with a negative exponent?
    Community Answer
    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.
  • Question
    What is 400 divided by 10^3?
    Community Answer
    400 / 10³ = 400 / 1000 = 0.4.
  • Question
    What do I do with whole numbers that don't divide into each other?
    Community Answer
    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.
  • Question
    What is 4/3 to the power 4 divided by 2/9 to the power 4?
    Community Answer
    (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
  • Question
    How do I divide a bionomial numerator with has no exponents with denominator with the same base as the numerator, but with negative exponents x + y / x1 + y1?
    Donagan
    Top Answerer
    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.
  • Question
    What is (8/9) to the 2nd exponent? Is it 64/81?
    Donagan
    Top Answerer
    Yes. (8/9)² = 8² / 9² = 64 / 81.
  • Question
    How do I divide exponents with different bases?
    Donagan
    Top Answerer
    First evaluate each base-and-exponent pair, then do the division. For example, 2^8 / 3³ = 256 / 27 = 9.48.
  • Question
    How do I multiply 2^6 * 5^5?
    Donagan
    Top Answerer
    (2^6)(5^5) = (64)(3125) = 200,000.
  • Question
    How can I calculate -2 to the power of 2 divided by 3?
    Donagan
    Top Answerer
    (-2)² / 3 = 4 / 3.
  • Question
    What is 3 to power of 4 divided by 3 to the power of 4?
    Donagan
    Top Answerer
    Any number divided by itself equals 1.
  • Question
    6 x 6 x 6 should be divided by what number to get 3 x 3 x 3 x 3?
    Donagan
    Top Answerer
    6 x 6 x 6 = 216. 3 x 3 x 3 x 3 = 81. Divide 216 by 81.
  • Question
    What's another way of writing a^(m/n)?
    Donagan
    Top Answerer
    [a^m]^(1/n). This means the nth root of (a^m).
  • Question
    How to divide y^2/y^3
    SamJ1307
    Community Answer
    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.
  • Question
    How do I divide a^x by b^y?
    Community Answer
    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).
  • Question
    What (is x³+3x²+1) divided by (x² - x + 1)?
    Community Answer
    This is a polynomial divided by a polynomial. See Divide Polynomials and Divide Polynomials Using Synthetic Division
  • Question
    What is 5 x 10^9 divided by 1 x 10^10?
    Community Answer
    (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.
  • Question
    How do you divide x^2 /x^3?
    Community Answer
    x² / x³ = x^(2 - 3) = x^(-1) = 1 / x^(1) = 1 / x.
  • Question
    What do I do when the denominator is larger, and I end up with negative values?
    Community Answer
    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.
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