Exponent Fraction Simplifier
Simplifies fractions containing exponents using the Quotient Rule. Handles negative exponents by rearranging terms.
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About
When dividing terms with exponents, understanding the movement of bases is key. The Quotient Rule states that you subtract the exponent of the denominator from the exponent of the numerator. However, the resulting negative exponents often confuse students.
This tool automates the process of subtraction and subsequent rearrangement. It ensures that the final answer contains only positive exponents, which is the standard requirement in academic algebra. It explicitly handles the case where x−n becomes 1xn.
exponents
quotient rule
powers
negative exponents
algebra
Formulas
The simplification logic follows strict laws of indices:
{
xaxb = xa−bx−n = 1xn(xy)n = xnyn
Reference Data
| Expression | Rule Applied | Intermediate Step | Final Result |
|---|---|---|---|
| x5x2 | a − b | x5−2 | x3 |
| x2x5 | Negative Exp | x2−5 = x−3 | 1x3 |
| x3x3 | Zero Exp | x0 | 1 |
| x−2y3 | Move Negative | (Move x down) | 1x2y3 |
Frequently Asked Questions
Any non-zero base raised to the power of zero equals 1. This is because x^a / x^a = 1, and also equals x^(a-a) = x^0.
A negative exponent indicates the reciprocal. Just as 10^-1 is 1/10, x^-n is mathematically defined as 1/x^n to maintain consistency with subtraction rules.
No. The bases (x and y) are different. The quotient rule only applies when the bases are identical.