Simplifying Expressions with Exponents Practice

Practice Objectives

Demonstrate the ability to simplify exponential expressions using the product rule for exponents
Demonstrate the ability to simplify exponential expressions using the quotient rule for exponents
Demonstrate the ability to simplify exponential expressions using the power rules for exponents
Demonstrate the ability to simplify exponential expressions with negative exponents
Demonstrate the ability to simplify exponential expressions with an exponent of zero

Practice Simplifying Exponential Expressions Using the Rules of Exponents

Instructions:

Answer 7/10 questions correctly to pass.

Simplify by writing with positive exponents. Assume that all variables represent nonzero real numbers.

Problem:

Correct!

Not Correct!

Your answer was: 0

The correct answer was: 0

For any Integers m and n:

Product Rule:
- $$a^m \cdot a^n = a^{m \, + \, n}$$
Quotient Rule:
- $$\frac{a^m}{a^n} = a^{m \, - \, n}, a ≠ 0$$
Exponent of Zero:
- $$a^0 = 1, a ≠ 0$$
Negative Exponent:
- $$a^{-n} = \frac{1}{a^n}, a≠ 0$$
Power Rules:
- $$\left(a^m\right)^n = a^{mn}$$
- $$\left(ab\right)^m = a^mb^m$$
- $$\left(\frac{a^m}{b^m}\right) = \frac{a^m}{b^m}, b ≠ 0$$