How to Calculate Exponents

By Ida Tolen; Updated April 24, 2017
Math Calculations.

Most high school students learn to calculate exponents in their algebra classes. Many times, students do not realize the importance of exponents. The use of exponents is just a simple way to perform repeated multiplication of a number by itself. Students need to know about exponents to solve certain types of algebra problems, such as scientific notation, exponential growth and exponential decay problems. You can learn to calculate exponents easily, but you will first need to know some basic rules.

Understand that you express a power in terms of a base and an exponent. The base B represents the number you multiply and the exponent "x" tells you how many times you multiply the base, and you write it as "B^ x." For example, 8^3 is 8X8X8=512 where "8" is the base, "3" is the exponent and the whole expression is the power.

Know that any base B raised to the first power is equal to B, or B^1 = B. Any base raised to the zero power (B^0) is equal to 1 when B is 1 or greater. Some examples of these are "9^ 1=9" and "9^0=1."

Add exponents when you multiply 2 terms with the same base. For example, [(B^3) x (B^3)] = B^ (3+3) = B^6. When you have an expression, such as (B^4) ^4, where an exponent expression is raised to a power, you multiply the exponent and the power (4x4) to get B^16.

Express a negative exponent like B raised to the negative 3 or (B^ -3) as a positive exponent by writing it as 1/ (B^3) to solve it. As an example, take "4^ -5" and rewrite it as "1/ (4 ^ 5) =1/1024 =0.00095."

Subtract the exponents when you have a division of 2 exponent expressions with the same base, such as "B^m)/ (B^n)" to get "B^ (m-n)." Remember to subtract the exponent that is on the bottom expression from the exponent that is on the top expression.

Express exponent expression with fractions like (B^n/m) as the mth root of B raised to the nth power. Solve 16^2/4 using this rule. This becomes the fourth root of 16 raised to the second power or 16 squared. First, square 16 to get 256 and then take the fourth root of 256 and the result is 4. Note that if you simplify the fraction 2/4 to 1/2, then the problem becomes 16^1/2 which is just the square root of 16 which is 4. Knowing these few rules can help you to calculate most exponent expressions.