Learn on PengienVision, Mathematics, Grade 6Chapter 3: Numeric and Algebraic Expressions

Lesson 1: Understand and Represent Exponents

In this Grade 6 lesson from enVision Mathematics Chapter 3, students learn to write and evaluate numbers with exponents by identifying the base, exponent, and power in expressions such as 2³ and 5⁴. Students practice converting repeated multiplication into exponential form, evaluating powers including zero exponents and decimal bases, and applying exponents in expressions like 1.9 × 10⁵. The lesson aligns with Common Core Standard 6.EE.A.1 on writing and evaluating numerical expressions involving whole-number exponents.

Section 1

Exponents

Property

An exponent is a number that appears above and to the right of a particular factor. It tells us how many times that factor occurs in the expression. The factor to which the exponent applies is called the base, and the product is called a power of the base.
An exponent indicates repeated multiplication.

a^n = a \cdot a \cdot a \cdots a \quad (n \text{ factors of } a)

where $n$ is a positive integer.

Examples

To compute $5^3$ , we multiply three factors of 5: $5 \cdot 5 \cdot 5 = 125$ .

The expression $(\frac{1}{4})^2$ means $\frac{1}{4} \cdot \frac{1}{4} = \frac{1}{16}$ .

Section 2

The Zero Exponent Rule

Property

For any non-zero number $a$ , a number raised to the power of zero is equal to 1.

a^0 = 1 \quad (\text{for } a \neq 0)

Examples

Section 3

Exponents with Decimal and Fractional Bases

Property

The rule of repeated multiplication applies to any base, including decimals and fractions. For a fractional base, the exponent applies to both the numerator and the denominator.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Exponents

Property

a^n = a \cdot a \cdot a \cdots a \quad (n \text{ factors of } a)

where $n$ is a positive integer.

Examples

To compute $5^3$ , we multiply three factors of 5: $5 \cdot 5 \cdot 5 = 125$ .

The expression $(\frac{1}{4})^2$ means $\frac{1}{4} \cdot \frac{1}{4} = \frac{1}{16}$ .

Section 2

The Zero Exponent Rule

Property

For any non-zero number $a$ , a number raised to the power of zero is equal to 1.

a^0 = 1 \quad (\text{for } a \neq 0)

Examples

Section 3

Exponents with Decimal and Fractional Bases

Property

The rule of repeated multiplication applies to any base, including decimals and fractions. For a fractional base, the exponent applies to both the numerator and the denominator.

Examples

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

Section 1

Exponents

Property

a^n = a \cdot a \cdot a \cdots a \quad (n \text{ factors of } a)

where $n$ is a positive integer.

Examples

To compute $5^3$ , we multiply three factors of 5: $5 \cdot 5 \cdot 5 = 125$ .

The expression $(\frac{1}{4})^2$ means $\frac{1}{4} \cdot \frac{1}{4} = \frac{1}{16}$ .

Section 2

The Zero Exponent Rule

Property

For any non-zero number $a$ , a number raised to the power of zero is equal to 1.

a^0 = 1 \quad (\text{for } a \neq 0)

Examples

Section 3

Exponents with Decimal and Fractional Bases

Property

The rule of repeated multiplication applies to any base, including decimals and fractions. For a fractional base, the exponent applies to both the numerator and the denominator.