Practice Objectives
  • Demonstrate an understanding of the product rule for exponents
  • Demonstrate an understanding of the power to power rule for exponents
  • Demonstrate an understanding of the product to a power rule for exponents
  • Demonstrate an understanding of the quotient to a power rule for exponents

Practice Simplifying Expressions Using the Product & Power Rules for Exponents


Instructions:

Answer 7/10 questions correctly to pass.

Simplify each expression and enter the correct exponent values in the given input fields.


Problem:

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The Product Rule for Exponents:

  1. When we multiply two or more exponential expressions with the same base:
    • Keep the common base
    • Add the exponents
  2. $$x^a \cdot x^b = x^{a + b}$$

The Power Rules for Exponents:

  1. To raise a power to a power:
    • Leave the base unchanged
    • Multiply the exponents
    • $$\left(x^a\right)^b = x^{ab}$$
  2. To raise a product to a power:
    • Raise each factor to that power
    • $$\left(ab\right)^c = a^cb^c$$
  3. To raise a quotient to a power:
    • Raise the numerator and denominator to that power
    • $$\left(\frac{a}{b}\right)^c = \frac{a^c}{b^c}, b ≠ 0$$

Step-by-Step:


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$$a = $$
$$b = $$
$$c = $$
$$d = $$

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Wrong Answers: 0 of 3

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Wow! You have mastered The Product & Power Rules for Exponents!

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