An exponent represents the number of times a base number is multiplied by itself. It is denoted by a superscript number placed to the right and slightly above the base number. For example, in the expression 3^{4}, 3 is the base and 4 is the exponent. This means that 3 is multiplied by itself 4 times.

When evaluating exponents, there are some basic rules to keep in mind:

**Product of Powers:**When multiplying two numbers with the same base, you can add the exponents. For example, 3^{2}* 3^{4}= 3^{6}.**Quotient of Powers:**When dividing two numbers with the same base, you can subtract the exponents. For example, 6^{5}/ 6^{3}= 6^{2}.**Power of a Power:**When a number is raised to an exponent and then raised to another exponent, you can multiply the exponents. For example, (2^{3})^{4}= 2^{12}.**Zero Exponent:**Any non-zero number raised to the power of 0 is equal to 1. For example, 5^{0}= 1.**Negative Exponent:**A negative exponent indicates the reciprocal of the base raised to the positive exponent. For example, 4^{-2}= 1 / 4^{2}= 1 / 16.

Let's go through some examples to demonstrate how to evaluate exponents using the rules mentioned above:

- Evaluate 2
^{3}* 2^{5}: - Evaluate 9
^{4}/ 9^{2}: - Evaluate (5
^{2})^{3}: - Evaluate 7
^{0}: - Evaluate 8
^{-2}:

Using the product of powers rule, we add the exponents: 2^{3} * 2^{5} = 2^{8}.

Using the quotient of powers rule, we subtract the exponents: 9^{4} / 9^{2} = 9^{2}.

Using the power of a power rule, we multiply the exponents: (5^{2})^{3} = 5^{6}.

As per the zero exponent rule, any non-zero number raised to the power of 0 is equal to 1: 7^{0} = 1.

Using the negative exponent rule, we take the reciprocal of the base raised to the positive exponent: 8^{-2} = 1 / 8^{2} = 1 / 64.

Now, let's try some practice problems to reinforce the concepts:

- Evaluate 4
^{3}* 4^{2}. - Evaluate 10
^{5}/ 10^{3}. - Evaluate (6
^{4})^{2}. - Evaluate 2
^{0}. - Evaluate 3
^{-3}.

After solving these practice problems, you should have a better understanding of how to evaluate exponents using the rules and examples provided above.

Study GuideEvaluate Exponents Worksheet/Answer key

Evaluate Exponents Worksheet/Answer key

Evaluate Exponents Worksheet/Answer key

Evaluate Exponents

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation.