# What happens when you divide exponents? General rules

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160 The number of times a variable or number has been multiplied by itself is represented as an exponent. Simplifying expressions is made easier by the rules of exponents. When dividing exponents with the same base, the basic rule is to remove the provided powers. This is also known as the Exponent Quotient Property. There are a few exponent rules that might aid with exponent division. These methods can also be used to simplify numbers that have complicated powers, such as fractions, decimals, and roots.

For example, we may use the rule to divide integers or variables with the same base.

am ÷ an = am-n

Likewise, we use the rule to split integers or variables with various bases.

am ÷ bm = (a ÷ b)m

So, when bases are the same, you can divide exponential expressions and get exponential expressions as the results. Then, subtract the exponents to divide exponents (or powers) with the same base. Multiplication is the inverse of division. Therefore, it makes logical that when multiplying numbers with the same basis, you add exponents, and when dividing numbers with the same base, you remove exponents.

## How to divide exponents with the same and different bases?

We utilize the basic rule of subtracting powers to divide exponents with the same base. For example, consider the am ÷ an formula, where an is the common base and m and n are the exponents.

The ‘Power of quotient property‘ is used to divide exponents with various bases and the same exponent. For example, consider the case am ÷ bm, where the bases of the expressions are different, but the exponent is the same.

## How to divide negative exponents?

negative exponent indicates that a base is on the fraction line’s denominator side. In other words, the negative exponent rule states that a negative exponent number should be placed in the denominator and vice versa. Negative exponents are divided in a similar way to positive exponents. Only you’re doing the opposite: subtracting where you’d add and dividing where you’d multiply. Also, we can say that if the bases are the same, we need to subtract the exponents. If necessary, reverse the exponent and make it positive. Divide the bases first if the exponents are the same, but the bases are different. If you can’t find anything in common, move on to solving the problem.

## Dividing exponents calculator

When you need to compute a quotient of two exponents, our Dividing Exponent Calculator (https://calconcalculator.com/math/dividing-exponents-calculator/)is here to help. You may learn how to divide exponents step by step with our calculator. The quotient is determined by the calculator. You must enter data, such as the bases x and y, as well as the exponents a and b, into the appropriate areas. Our calculator for dividing exponents provides a step-by-step answer to your problem. Our calculator can approximate their decimal values if the final result contains fractions. The precision with which the dividing exponent’s calculator approximates the fractions may also be increased.

## How to divide fraction exponents? Fraction exponent calculator

fractional exponent is when the exponent of a number is a fraction. Exponents represent the number of times reproduced in multiplication. Subtract the exponent you’re dividing (the divisor) from the one you’re dividing to solve divisions of two integers with fractional exponents (the dividend). This is because every number divided by itself equals one, which corresponds to the well-known fact that any integer multiplied by a power of 0 equals 1. You can get fractional exponents with a number other than one in the numerator, just like you can get fractional exponents with a number other than one in the numerator.

Our Fraction Exponent Calculatorcan assist you with fractional exponents (surprise, surprise). If you wish to use this calculator as a basic exponent calculator, enter 1 as the denominator and an integer as the exponent instead of a fraction. You can check it out on https://calconcalculator.com/math/fraction-exponent-calculator/.