Expressions with exponents; order of operations

Warm-up

Three quick questions from earlier lessons.

Discover

What is $3^4$ ?

Key idea

Exponents mean repeated multiplication; they come first.

b^n

means

n

factors of

b

b \cdot b \cdots b

. Order of operations: parentheses, then exponents, then multiplication and division, then addition and subtraction. In

3x^2

only

x

is squared.

Worked example

Evaluate $2 + 3 \cdot 4^2$ .

4^2 = 16

Exponent first.

3 \cdot 16 = 48

Multiply.

50

Add.

Your turn, guided

Your turn: $5x^2$ when $x = 3$ .

45

5 · 9.

Practice ★

What is the value of $6^{ 4 }$ ?
What is the value of $6^{ 2 }$ ?

Evaluate $1 + 2 \cdot 3^2$ .

Watch out!

Practice ★★

Evaluate $4x^2$ when $x = 8$ .
Evaluate $4x^2$ when $x = 4$ .

Boss problem. A square garden has side 10 m. A path 1 m wide goes all around it, making a bigger square.

Exit ticket

Three questions to check you have got it.

Evaluate $1 + 2 \cdot 3^2$ .
Evaluate $5 + 5 \cdot 2^2$ .
Evaluate $1 + 3 \cdot 2^2$ .

Summary card

Expressions with exponents

Parentheses, exponents, × ÷, + −.

Watch out: in kx² only x is squared.

End of the lesson

Next lesson: Proportional relationships: y = kx Back to the chapter

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