Learn on PengiPengi Math (Grade 7)Chapter 2: Rational Numbers and Exponents

Lesson 5: Exponents and Order of Operations

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.

Section 1

Introduction to 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.

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

where nn is a positive integer.

Examples

  • To compute −53-5^3, we multiply three factors of -5: −5⋅−5⋅−5=−125-5 \cdot -5 \cdot -5 = -125.
  • The expression (14)2(\frac{1}{4})^2 means 14⋅14=116\frac{1}{4} \cdot \frac{1}{4} = \frac{1}{16}.

Section 2

Order of Operations with Exponents

Property

When evaluating expressions containing exponents, follow the order of operations (PEMDAS): Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Pay special attention to the difference with negative bases:

  • (−a)n(-a)^n means the base is −a-a
  • −an-a^n means the base is aa, and you take the opposite of the result

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Introduction to 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.

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

where nn is a positive integer.

Examples

  • To compute −53-5^3, we multiply three factors of -5: −5⋅−5⋅−5=−125-5 \cdot -5 \cdot -5 = -125.
  • The expression (14)2(\frac{1}{4})^2 means 14⋅14=116\frac{1}{4} \cdot \frac{1}{4} = \frac{1}{16}.

Section 2

Order of Operations with Exponents

Property

When evaluating expressions containing exponents, follow the order of operations (PEMDAS): Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Pay special attention to the difference with negative bases:

  • (−a)n(-a)^n means the base is −a-a
  • −an-a^n means the base is aa, and you take the opposite of the result