How to Simplify Exponents

Exponents are a shorthand for repeated multiplication. The rules help you simplify expressions without writing every factor.

Quick idea

Exponent rules work because powers count how many repeated factors are being multiplied.

Steps

1. When multiplying powers with the same base, add exponents.
2. When dividing powers with the same base, subtract exponents.
3. When raising a power to another power, multiply exponents.
4. Rewrite negative exponents as reciprocals.

Worked example

Simplify x to the third times x to the fourth.

Full solution

Step-by-step walkthrough

Step 1

Both powers have the same base, x.

Step 2

Add the exponents 3 and 4.

Step 3

The result is x to the seventh.

Common mistake

Only add exponents when the bases are the same and the operation is multiplication.

Practice problems

1. Simplify x^2 x^5.
2. Simplify y^8 / y^3.
3. Simplify (a^4)^2.

Answers

1. x^7
2. y^5
3. a^8

Ask Pennpaper to explain it live

If the steps make sense but you still feel stuck, start a Pennpaper lesson and ask the tutor to draw the problem on the whiteboard. Seeing the symbols move step by step is often what makes the concept click.

Related guides

• How to Factor Quadratics
• The Quadratic Formula Explained
• Order of Operations Explained