Multiply Terms with Exponents

CONCEPTS

Properties

• (ab)ˣ = aˣ * bˣ

• aˣ * aʸ = aˣ ⁺ ʸ

Tips

• Follow order of operations (PEMDAS)…exponents are after parentheses

(PEMDAS stands for parentheses, exponents, multiplication, division, addition, and subtraction. Complete all mathematical operations in this order.)

• Exponents are used to simplify an expression when the same number is multiplied together 2 * 2 * 2 * 2 * 2 = 2⁵

There are 3 ways of looking at exponent expressions:

• a³ + a³ = 2a³

• a³ * a³ = a³⁺³ = a⁶

• (a³)³ = a³*³ = a⁹

• The trick is the base (a) must be the same when performing these operations!

• ALWAYS Group terms when there are exponent expressions. This is the key to solving exponent expressions…1) negatives, 2) numbers, 3) exponents with common bases

Examples: –(5a² b⁴)² * (–4 a²)⁴ = –(25 a⁴ b⁸) * (256 a⁸) = (–)(25 * 256)(a⁴ a⁸)(b⁸) = –6400 a¹² b⁸

PRACTICE PROBLEMS

Question 1 Are the expression (-a)² and -(a)² equivalent?

-- Answer -- (ab)ˣ

aˣ * bˣ = (ab)ˣ

Question 2 Rewrite aˣ * bˣ with 1 exponent, rather than 2

-- Answer -- -8 a³ b⁵ + -4 a⁴ b²

-4a³ * 2b⁵ + 4a³ * -ab² = (-4*2) * (a³) * (b⁵) + (-4) * (a³ * a) * (b²) = -8 a³ b⁵ + -4 a⁴ b²

Question 3 Simplify -4a³ (2b⁵ - ab²)?

-- Answer -- 3⁶

The bases must be common to add exponents. 9 can be rewritten as 3², so the expression can be written 3² * (3²)² = 3² * 3⁴ = 3²⁺⁴ = 3⁶

Question 4 What is 3² * 9²?

-- Answer -- 3⁶

3² * 9² = 3² * (3²)² = 3² * = 3⁴ = 3⁶

ACT PRACTICE PROBLEMS