Evaluate numerical expressions involving exponents

Key notes:

Definition of Exponents

  • An exponent represents repeated multiplication of a base number.
  • Example: 34 = 3 × 3 × 3 × 3 = 81.

Parts of an Exponential Expression

  • Base: The number being multiplied (e.g., 3 in 34).
  • Exponent: The small number above the base indicating the number of times to multiply (e.g., 4 in 34).

Evaluating Expressions with Exponents

  • Follow the order of operations (PEMDAS/BODMAS).
  • Compute exponents before multiplication, division, addition, or subtraction.
  • Example: 2 + 32 = 2 + 9 = 11.

Properties of Exponents

  • Product Rule: am × an = am+n.
  • Quotient Rule: am ÷ an = am−n, where m>n.
  • Power Rule: (am)n = am×n.
  • Zero Exponent Rule: a0 = 1 (any nonzero number raised to 0 is 1).
  • Negative Exponent Rule: a−n = 1an.

Evaluating Expressions with Different Operations

Example: 43 − 22

  • 43 = 4 × 4 × 4 = 64.
  • 22 = 2 × 2 = 4.
  • 64 − 4 = 60.

Using Exponents in Real-Life Problems

  • Square and cube numbers in geometry and physics.
  • Exponential growth in populations and finance.

Common Mistakes to Avoid

  • Misinterpreting aba^bab as a×ba \times ba×b.
  • Forgetting the order of operations.
  • Incorrectly applying exponent rules.

Learn with an example

➡️ Evaluate the expression.

22 × 1

First, identify the operations in the expression .

22 x 1

This expression has an exponent. It also has multiplication. The order of operations says to evaluate the exponent before multiplying.

22 × 1

= 4 × 1

Now, multiply.

4 × 1

= 4

The value of the expression is 4.

➡️ Evaluate the expression.

5 × 32

First, identify the operations in the expression.

5 × 32

This expression has an exponent. It also has multiplication. The order of operations says to evaluate the exponent before multiplying.

5 × 32

= 5 × 9

Now, multiply.

5 × 9

= 45

The value of the expression is 45.

➡️ Evaluate the expression.

3 – 42

First, identify the operations in the expression.

3 – 42

This expression has an exponent. It also has subtraction. The order of operations says to evaluate the exponent before subtracting.

3 – 42

= 3 – 16

Now, subtract.

3 – 16

= –13

The value of the expression is – 13.

let’s practice! 🖊️