Word Problems Involving Exponents Study Guide (page 2)

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Updated on Oct 4, 2011

Negative Exponents

A negative exponent tells you to take the reciprocal of the base. For example,. For expressions to be simplified, they should be written with positive exponents.

Converting to and From Scientific Notation and Standard Form

Scientific Notation

Scientific notation is used to write very large and very small numbers in a more efficient manner. This form uses a number between one and ten and multiplies it by a power of 10. For example, the number 3,000,000,000 is written as 3 × 109 in scientific notation.

Converting From Standard Form to Scientific Notation

To change a number from standard form into scientific notation, take the first non-zero digit and place a decimal point to its right to form a value between 1 and 10. Then, multiply by a power of 10, where the exponent is the number of places the decimal point moves.

For example, to write the number 4,500,000 in scientific notation, use the digits 4 and 5 and write the decimal 4.5. Because the decimal point needs to move six places to the left to be between the 4 and 5, the exponent is 6. The scientific notation is 4.5 × 106.

Converting From Scientific Notation to Standard Form

To convert to standard form from scientific notation, reverse the process just explained. Write the value between one and 10, but move the decimal point as according to the exponent.

For example, for the value 3.42 × 10–4, first write the number 3.42. Then, move the decimal to the right if the exponent is positive or to the left if the exponent is negative. Use zeros as placeholders when necessary. Since this exponent is –4, move the decimal four places to the left. The standard form is 0.000342.


When you are converting from standard form to scientific notation, numbers greater than one have a positive exponent and numbers less than one have a negative exponent.

Word Problems with Exponents

The word problems in this section involve using the properties of exponents. Use the information in this lesson and the problem solving steps to solve each one.

Example 1

What is the product of 105× 108?

Read and understand the question. This question is looking for the product of two values that have the same base.

Make a plan. Add the exponents to find the solution.

Carry out the plan. The problem becomes 105× 108= 105 + 8 = 1013.

Check your answer. To check your answer, divide the product by one of the factors that was multiplied in the question.

Because this was the other factor, this answer is checking.

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