- The Power Rule for Powers
- The Power Rule for Products
- The Power Rule for quotients

Inside Collection (Textbook): Basic Mathematics Review

Summary: This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. The symbols, notations, and properties of numbers that form the basis of algebra, as well as exponents and the rules of exponents, are introduced in this chapter. Each property of real numbers and the rules of exponents are expressed both symbolically and literally. Literal explanations are included because symbolic explanations alone may be difficult for a student to interpret. Objectives of this module: understand the power rules for powers, products, and quotients.

- The Power Rule for Powers
- The Power Rule for Products
- The Power Rule for quotients

The following examples suggest a rule for raising a power to a power:

Using the product rule we get

If

To raise a power to a power, multiply the exponents.

Simplify each expression using the power rule for powers. All exponents are natural numbers.

Although we don’t know exactly what number

Simplify each expression using the power rule for powers.

The following examples suggest a rule for raising a product to a power:

If

To raise a product to a power, apply the exponent to each and every factor.

Make use of either or both the power rule for products and power rule for powers to simplify each expression.

Make use of either or both the power rule for products and the power rule for powers to simplify each expression.

The following example suggests a rule for raising a quotient to a power.

If

To raise a quotient to a power, distribute the exponent to both the numerator and denominator.

Make use of the power rule for quotients, the power rule for products, the power rule for powers, or a combination of these rules to simplify each expression. All exponents are natural numbers.

Make use of the power rule for quotients, the power rule for products, the power rule for powers, or a combination of these rules to simplify each expression.

Use the power rules for exponents to simplify the following problems. Assume that all bases are nonzero and that all variable exponents are natural numbers.

1

*((Reference))* Is there a smallest integer? If so, what is it?

no

*((Reference))* Use the distributive property to expand

*((Reference))* Find the value of

147

*((Reference))* Assuming the bases are not zero, find the value of

*((Reference))* Assuming the bases are not zero, find the value of

- « Previous module in collection Rules of Exponents
- Collection home: Basic Mathematics Review
- Next module in collection » Summary of Key Concepts

Comments:"Reviewer's Comments: 'I recommend this book for courses in elementary algebra. The chapters are fairly clear and comprehensible, making them quite readable. The authors do a particularly nice job […]"