# Can you subtract exponents with the same base?

Table of Contents

## Can you subtract exponents with the same base?

When two exponents with the same base are being divided, subtract the exponent of the denominator from the exponent of the numerator to yield a new exponent. Attach that exponent to the base, and that is your answer. In this case, subtract from . That yields as the new exponent and as the answer.

**What do you do when two exponents have the same base?**

To divide exponents that have the same base, keep the same base and subtract the power of the denominator from the power of the numerator. If the terms of an expression have the same power but different bases, divide the bases then raise the result to the power.

**How do you simplify exponents with the same base?**

To simplify a power of a power, you multiply the exponents, keeping the base the same. For example, (23)5 = 215. For any positive number x and integers a and b: (xa)b= xa· b. Simplify.

### What happens when an exponent is a fraction?

When the exponent is a fraction, you’re looking for a root of the base. The root corresponds to the denominator of the fraction. For example, take “125 raised to the 1/3 power,” or 125^1/3. The denominator of the fraction is 3, so you’re looking for the 3rd root (or cube root) of 125.

**What if both base and exponent are same?**

Answer: The exponent “product rule” tells us that, when multiplying two powers that have the same base, you can add the exponents.

**When exponents are the same and bases are different?**

When multiplying exponents with different bases and the same powers, the bases are multiplied first. It can be written mathematically as an × bn = (a × b)n. Example: Find the product of 52 and 82. Solution: Here, the bases are different but the powers are the same.

#### When bases are same powers are equal?

When two exponential terms with the same base are multiplied, their powers are added while the base remains the same. However, when two exponential terms having the same base are divided, their powers are subtracted.

**What if power is same and base are different?**