← Algebra I

Algebra I

Exponent Rules

Lesson

An exponent tells you how many times to multiply the base by itself. x3x^3 means x⋅x⋅xx \cdot x \cdot x. Three rules let you simplify expressions with exponents quickly.

Rule 1: Product rule (same base)

xa⋅xb=xa+bx^a \cdot x^b = x^{a+b}

When you multiply same-base powers, add the exponents. Example: x2⋅x3=x5x^2 \cdot x^3 = x^5.

Rule 2: Quotient rule (same base)

xaxb=xa−b\frac{x^a}{x^b} = x^{a-b}

When you divide same-base powers, subtract the exponents. Example: x7x3=x4\frac{x^7}{x^3} = x^4.

Rule 3: Power of a power

(xa)b=xa⋅b(x^a)^b = x^{a \cdot b}

When you raise a power to another power, multiply the exponents. Example: (x2)3=x6(x^2)^3 = x^6.

How to type your answer

Use a caret ^ for exponents. No spaces. Examples: x^5, y^7, x^12.

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

Quick problems to get going.

Problem 1

x⋅xx \cdot x

Problem 2

y3⋅yy^3 \cdot y

Problem 3

x4x\frac{x^4}{x}

Problem 4

(a2)2(a^2)^2

Practice

Standard problems matching the lesson.

Problem 5

x3⋅x4x^3 \cdot x^4

Problem 6

x2⋅x5x^2 \cdot x^5

Problem 7

y6⋅yy^6 \cdot y

Problem 8

a4⋅a4a^4 \cdot a^4

Problem 9

x8x3\frac{x^8}{x^3}

Problem 10

y10y4\frac{y^{10}}{y^4}

Problem 11

a9a2\frac{a^9}{a^2}

Problem 12

x12x7\frac{x^{12}}{x^7}

Problem 13

(x2)3(x^2)^3

Problem 14

(y4)2(y^4)^2

Problem 15

(a3)5(a^3)^5

Problem 16

x2⋅x3⋅xx^2 \cdot x^3 \cdot x

Challenge

Harder problems — edge cases, trickier numbers, multiple steps.

Problem 17

x5⋅x2⋅xx^5 \cdot x^2 \cdot x

Problem 18

(x3)2⋅x(x^3)^2 \cdot x

Problem 19

(a2)4a3\frac{(a^2)^4}{a^3}

Problem 20

x⋅x2⋅x3⋅x4x \cdot x^2 \cdot x^3 \cdot x^4

Problem 21

(y4)2⋅y3(y^4)^2 \cdot y^3

Problem 22

x15(x3)2\frac{x^{15}}{(x^3)^2}

Practice

Standard problems matching the lesson.

Problem 23

A photo file is x^2 KB. Enlarging multiplies the size by x^3. Write the new size as a single power of x.

Problem 24

A square garden has side x^4 meters. Express its area as a single power of x.

Challenge

Harder problems — edge cases, trickier numbers, multiple steps.

Problem 25

A cube has volume V = (x^2)^3 cubic feet. Simplify V as a single power of x.

Ask the tutor

Stuck on a concept? Want another example? Ask anything about this topic.

Type your own question below, or tap one of the suggestions. The tutor can re-explain the lesson, work through a specific problem with you, generate fresh practice tuned to where you are, or check your reasoning.

Quiz

Test yourself on this topic →

10 questions, no hints. About 5 minutes.