Evaluating Exponential Expressions

\( \sqrt{9} = 3 = \frac{3}{1}\), \( \sqrt{16} = 4 = \frac{4}{1}\)

Evaluating Exponential Expressions
Evaluating exponential expressions means finding the numerical value of an expression that contains a base raised to a power (exponent). The process depends on whether the base and exponent are constants, variables, integers, fractions, or negative numbers.

Look at the following lesson if you need to review the rules of exponents for the different types of exponents:
Rules of Exponents

When evaluating more complex expressions involving exponents, remember to follow the order of operations (PEMDAS/BODMAS):

1. Parentheses (or Brackets)
2. Exponents (or Orders)
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)

If the base or exponent contains variables, you can only evaluate the expression if the values of those variables are given.

1. When possible, simplify the expression using the rules of exponents.
   
2. Substitute in the values for the variables and solve.

The following diagram gives some examples of evaluating exponential expressions. Scroll down the page for more examples and solutions.

 

• Worksheets to Practice Exponent Rules

  Printable
  Product Rule
  Quotient Rule
  Power Rule
  Negative Exponents
  Fractional exponents
  Laws of Exponents
  

  Online
  Apply Law of Exponents (multiply)
  Apply Law of Exponents (mixed)
  

Key Reminders:

• Order of Operations: Always follow PEMDAS/BODMAS. Exponents are evaluated before multiplication and division.
• Negative Bases: Pay close attention to parentheses when a negative number is raised to a power. ((-a)ⁿ) is different from (-aⁿ).
• Negative Exponents: Remember that (a^-n = 1/aⁿ).

Evaluating Algebraic Expressions with Exponents
Example:

1. Evaluate 4x² when x = 3
   
2. Evaluate x³ - 5x + 25

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Evaluating exponential expressions
Example:
Evaluate 5y⁴ - y² when y = 3

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Evaluating exponential expressions 2
Evaluate the expression 4n¹ - 2n⁰ for n = 1 and n = 5.

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Evaluating exponential expressions 3
Rewrite the following expression as the product of positive exponents, and then evaluate the expression when x = 2.
x^-35^-2x²

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