Apply the quotient rule for exponents: aᵐ / aⁿ = aᵐ⁻ⁿ.
Last updated: March 2026 | By ForgeCalc Engineering
When dividing two powers with the same base, you can simplify the expression by subtracting the exponent of the denominator from the exponent of the numerator. This is known as the Quotient Rule for Exponents.
This rule works because division is the inverse of multiplication. Just as you add exponents when multiplying powers with the same base, you subtract them when dividing.
This rule only applies when the bases are identical.
Simplify 2⁵ / 2³:
1. Identify base: 2
2. Subtract exponents: 5 - 3 = 2
3. New expression: 2²
4. Calculate: 2 * 2 = 4
Final Answer: 4
If m = n, then $a^m / a^n = a^{m-n} = a^0$. Any non-zero number raised to the power of 0 is 1.
You will get a negative exponent. For example, $2^3 / 2^5 = 2^{-2}$, which is equal to $1 / 2^2 = 1/4$.
Yes, as long as the bases are identical. For example, $(-3)^4 / (-3)^2 = (-3)^{4-2} = (-3)^2 = 9$.
The quotient rule does not apply if the bases are different. You must calculate each power individually or find another way to simplify.
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