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### Exponents and Scientific Notation

Section 1: Product Rule, Quotient Rule, and Power Rules Section 2: Zero Exponents and Negative Exponents Section 3: Scientific Notation Section 4: Rational Exponents Dr. Bump’s Videos on Exponents and Scientific Notation

# Math Review

## Exponents and Scientific Notation

### It Is Important That You Watch This Video First

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Negative exponents and zero exponents often show up when applying formulas or simplifying expressions.

In this section, we will define the Negative Exponent Rule and the Zero Exponent Rule and look at a couple of examples.

Negative Exponent Rule: In other words, when there is a negative exponent, we need to create a fraction and put the exponential expression in the denominator and make the exponent positive. For example, But working with negative exponents is just rule of exponents that we need to be able to use when working with exponential expressions.

Example:

Simplify: 3-2

Solution:

3-2 = Example:

Simplify: Solution:

Apply the Negative Exponent Rule to both the numerator and the denominator. Example:

Simplify: 3-1 + 5-1

Solution:

Apply the Negative Exponent Rule to each term and then add fractions by finding common denominators. Zero Exponent Rule: a0 = 1, a not equal to 0. The expression 00 is indeterminate, or undefined.

In the following example, when we apply the product rule for exponents, we end up with an exponent of zero.

x5x-5 = x5 + (-5) = x0

To help understand the purpose of the zero exponent, we will also rewrite x5x-5 using the negative exponent rule.

x5x-5 = The zero exponent indicates that there are no factors of a number.

Example:

Simplify each of the following expressions using the zero exponent rule for exponents. Write each expression using only positive exponents.

a) 30

b) -30 + n0

Solution:

a) Apply the Zero Exponent Rule.

30 = 1

b) Apply the Zero Exponent Rule to each term, and then simplify. The zero exponent on the first term applies to the 3 only and not the negative in front of the 3.

-30 + n0 =-(30) + n0 = – 1 + 1 = 0

Test Your Knowledge by opening up the Test Yourself Activity. « Basic Rules of Exponents | Math PREP Home | Scientific Notation » www.hccs.edu
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Click here . A negative exponent can be rewritten as a positive exponent if you take the reciprocal of the base. (a-2b3)-4    1     (a-2b3)4 First rewrite outside exponents as positive exponents.Did you notice that the base was everything inside the parenthesis? Click here . A negative exponent can be rewritten as a positive exponent if you take the reciprocal of the base. (a-2b3)-4    1     (a-2b3)4 First rewrite outside exponents as positive exponents.Did you notice that the base was everything inside the parenthesis?Clear the outside exponent by multiplying the base to itself four times.(a-2b3)(a-2b3)(a-2b3)(a-2b3) Click here . A negative exponent can be rewritten as a positive exponent if you take the reciprocal of the base. (a-2b3)-4    1     (a-2b3)4     1     a-8b12 First rewrite outside exponents as positive exponents.Did you notice that the base was everything inside the parenthesis?Clear the outside exponent by multiplying the base to itself four times.(a-2b3)(a-2b3)(a-2b3)(a-2b3) Click here . A negative exponent can be rewritten as a positive exponent if you take the reciprocal of the base. (a-2b3)-4    1     (a-2b3)4     1     a-8b12 First rewrite outside exponents as positive exponents.Did you notice that the base was everything inside the parenthesis?Clear the outside exponent by multiplying the base to itself four times.(a-2b3)(a-2b3)(a-2b3)(a-2b3)Are there any negative exponents left in the expression? Click here . A negative exponent can be rewritten as a positive exponent if you take the reciprocal of the base. (a-2b3)-4    1     (a-2b3)4     1     a-8b12 First rewrite outside exponents as positive exponents.Did you notice that the base was everything inside the parenthesis?Clear the outside exponent by multiplying the base to itself four times.(a-2b3)(a-2b3)(a-2b3)(a-2b3)Are there any negative exponents left in the expression? yes Click here . A negative exponent can be rewritten as a positive exponent if you take the reciprocal of the base. (a-2b3)-4    1     (a-2b3)4     1     a-8b12 First rewrite outside exponents as positive exponents.Did you notice that the base was everything inside the parenthesis?Clear the outside exponent by multiplying the base to itself four times.(a-2b3)(a-2b3)(a-2b3)(a-2b3)Are there any negative exponents left in the expression? yesWhat is the base of the negative exponent? Click here . A negative exponent can be rewritten as a positive exponent if you take the reciprocal of the base. (a-2b3)-4    1     (a-2b3)4     1     a-8b12 First rewrite outside exponents as positive exponents.Did you notice that the base was everything inside the parenthesis?Clear the outside exponent by multiplying the base to itself four times.(a-2b3)(a-2b3)(a-2b3)(a-2b3)Are there any negative exponents left in the expression? yesWhat is the base of the negative exponent? a Click here . A negative exponent can be rewritten as a positive exponent if you take the reciprocal of the base. (a-2b3)-4    1     (a-2b3)4     1     a-8b12 First rewrite outside exponents as positive exponents.Did you notice that the base was everything inside the parenthesis?Clear the outside exponent by multiplying the base to itself four times.(a-2b3)(a-2b3)(a-2b3)(a-2b3)Are there any negative exponents left in the expression? yesWhat is the base of the negative exponent? aWhat does the final result look like? Click here . A negative exponent can be rewritten as a positive exponent if you take the reciprocal of the base. (a-2b3)-4    1     (a-2b3)4     1     a-8b12 First rewrite outside exponents as positive exponents.Did you notice that the base was everything inside the parenthesis?Clear the outside exponent by multiplying the base to itself four times.(a-2b3)(a-2b3)(a-2b3)(a-2b3)Are there any negative exponents left in the expression? yesWhat is the base of the negative exponent? aWhat does the final result look like? Click here for another example.              