What if the exponent is zero?

Any number to the zero power is equal to 1 (a^0 = 1). This rule also applies when dividing powers if the numerator and denominator are equal.

Is it possible to divide powers with different bases?

Yes, but the exponent properties don't work here (if the exponents are also different). The calculator calculates each number separately and then divides the resulting values.

Division of powers

Instant calculation of the quotient of two powers with a solution

Enter expression

Division by zero is not possible

Fill in the reasons and indicators
to see the step-by-step solution

Result:

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💡 Rule

Division calculator

Q: How to divide powers with negative exponents?

The standard subtraction rule applies: a^m / a^-n = a^(m - (-n)) = a^(m + n). Minus by minus gives plus.

🎓 Power division calculator with solution

Operations with powers are the basis of algebra, but they often cause confusion, especially when negative exponents or different bases are introduced. Our tool helps you not only get an answer, but see a step-by-step solution.

🚀 How it works: The calculator automatically detects the type of example (same or different bases) and applies the correct formula. All you need to do is enter the numbers.

Basic rules that the algorithm uses

So that you can test yourself, here are the three main scenarios in which the program works:

Больше по теме: Root and power of a number

Degree ×🧮 How multiplication of powers works Our calculator helps you instantly solve examples with powers, showing not only the answer, but also the progress of the solution. This is useful for checking homework or engineering calculations.

1. Same reasons

The most common case at school. The base remains, the indicators are subtracted.

a^m / aⁿ = a^m-n

Example: 5⁸ / 5³ = 5⁵ = 3125

If you just need to calculate a number, use our exponentiation calculator.

2. Different reasons

There are no properties for simplification. You need to raise each number to a power separately, and then divide.

a^m / bⁿ

Example: 4³ / 2⁵ = 64 / 32 = 2

The algorithm can also work with negative powers (a^-n = 1/aⁿ). This is useful when preparing for the Unified State Exam and tests.

Where is this useful in life and study?

Finance: Formulas for discounting cash flows and calculations compound interest are based on the division of power functions (1+r)ⁿ.
Higher mathematics: Understanding the properties of powers is necessary for constructing graphs of functions and finding limits.
Solving systems: Often, when solving systems of equations using the substitution method, it is necessary to reduce variables in powers.

Frequently asked questions (FAQ)

🔹 What happens if the exponent is zero?

Any number (except zero) to the zero power is equal to one: a⁰ = 1. If, when dividing powers, the exponents are equal (for example, 5³ / 5³), then the power will be zero (3-3=0), and the answer will be 1.

🔹 How to divide powers with negative exponents?

The rule for subtracting indicators remains the same: a^m / a^-n = a^{m - (-n)} = a^{m + n}. That is, when dividing by a negative power, the indicators actually add up.

🔹 Is it possible to divide if the bases are different, but the indicators are the same?

Yes, there is a separate property for this: aⁿ / bⁿ = (a/b)ⁿ. You can first divide the bases, and then raise the result to a common power.