Skip to lesson

Choose “Save as PDF” in the print dialog to keep a copy.

Cogito

Integrated Math 1 · Chapter 4 · Lesson 3

Practice Worksheet

Properties of Exponents

The rules that make exponentials workable.

12 problems · about 20 minutes · N-RN.A.2, A-SSE.A.2

NameDate

Figure — use these to answer the problems

At x = 0 every exponential curve passes through its starting value, which is why the zero exponent gives 1.
-8-8-6-6-4-4-2-222446688
y = 1 · 2^x + 0
  • Point(0, 1)
a, starting amount1
b, base2
Point on the curve0
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. x⁶ · x³ = xⁿ. What is n?

    Answer

  2. Why does x⁰ equal 1?

    • Because x³ ÷ x³ is both 1 and x⁰.
    • It is an arbitrary convention.

  3. x² · x⁵ = xⁿ. What is n?

    Answer

  4. x⁹ ÷ x⁴ = xⁿ. What is n?

    Answer

  5. (x²)⁶ = xⁿ. What is n?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. What is 7⁰?

    Answer

  2. What is 2⁻³, as a decimal?

    Answer

  3. x⁴ ÷ x⁶ = xⁿ. What is n?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Match each operation with what it does to exponents.

    Draw a line from each item on the left to its match on the right.

    • Multiplying powers of the same base
    • Dividing powers of the same base
    • Raising a power to a power
    • Add the exponents
    • Subtract the exponents
    • Multiply the exponents

  2. What is 5⁻², as a decimal?

    Answer

  3. The Product

    x³ · x⁴ = xⁿ. What is n?

    Answer

  4. The Power

    (x³)⁴ = xⁿ. What is n?

    Answer