Practice Objectives
- Demonstrate the ability to simplify expressions with negative exponents
- Demonstrate the ability to simplify expressions using the product rule for exponents
- Demonstrate the ability to simplify expressions using the quotient rule for exponents
- Demonstrate the ability to simplify expressions using the power rules for exponents
Practice Simplifying Expressions with Negative Exponents
Instructions:
Answer 7/10 questions correctly to pass.
Simplify each by writing with positive exponents. Assume all variables represent nonzero real numbers.
Problem:
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Negative Exponents:
$$a^{-n} = \frac{1}{a^{n}}$$
- For any nonzero real number a and any integer n:
- Create a fraction with 1 as the numerator
- Move the base "a" into the denominator
- Change the exponent on "a" from "-n" to "n"
- In other words, take the reciprocal of the base with a positive exponent
The Product Rule for Exponents:
$$a^{m} \cdot a^{n} = a^{m + n}$$
- For any integers m and n:
- Keep the base the same and add the exponents
The Quotient Rule for Exponents:
$$\frac{a^{m}}{a^{n}} = a^{m - n}$$
- For any nonzero real number a and any integers m and n:
- Keep the base the same and subtract the exponents
The Power Rule for Exponents:
$$\left(a^m\right)^{n} = a^{mn}$$
- For any integers m and n:
- Keep the base the same and multiply the exponents
Step-by-Step:
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