Solve exponent expressions

CONCEPTS

Properties

• a⁰ = 1

• Whenever a function = 1, it can be equal to any base with a 0 exponent (ex: x⁰ = 1 or 5⁰ = 1)

Tips

• Exponents can be made equal when there is the same base (ex: 2ˣ = 2⁴, x = 4) because of the log property x = aʸ, y = logₐx

• Make the bases the same for all terms with exponents in the equation (ex: 4ˣ can be changed to (2²)ˣ or 2²ˣ)

PRACTICE PROBLEMS

Question 1 What is 3ˣ⁺⁴ if 3ˣ⁺¹ = 4

-- Answer -- 108

3ˣ⁺¹ = 3ˣ * 3¹

3ˣ⁺⁴ = 3ˣ * 3⁴ = 3ˣ⁺¹ * 3³ = 4 * 3³ = 108

Question 2 If 5ˣ⁺³ = 1, what is x?

-- Answer -- -3

1 = 5⁰ => this will make the same base for the 2 expressions. Any base with a zero exponent = 1

x+3 = 0, x = -3

ACT PRACTICE PROBLEMS

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