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Welcome to our Math lesson on Powers of Numbers Written in the Standard Form, this is the sixth lesson of our suite of math lessons covering the topic of Standard Form, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
Powers of Numbers Written in the Standard Form
If a number written in the standard form is raised to a certain power, we raise in that power only the numerical part before the power of ten, while the powers of ten multiply. This is just the application of properties of indices explained in Tutorial 7.1. In symbols, we have
(A × 10n )m = Am × 10n ∙ m
For example,
(2.7 × 105 )3 = (2.73 ) × 105 ∙ 3
= 19.683 × 1015
= 1.9683 × 1016
The same procedure is also used for numbers written in standard form when they are raised in a negative power. You just have to be careful when writing the sign of the result. For example,
(3.09 × 102 )-3 = (3.09-3 ) × 102 ∙ (-3)
≈ 0.0339 × 10-6
= 3.39 × 10-8
Example 6
The side length of a small cube is a = 1.84 mm. What is its volume in cubic metres? Volume of a cube is calculated by the formula V = a3. The conversion factor is 1 m = 1000 m.
Solution 6
First, we express the side length in metres. We have
a = 1.84 mm = 1.84 × 10-3 m
Thus,
V = a3 = (1.84 × 10-3 m)3
= (1.843 ) × (10-3 )3 m3
= 6.229504 × 10(-3) ∙ 3 m3
= 6.229504 × 10-9 m3
More Standard Form Lessons and Learning Resources
Powers and Roots Learning Material| Tutorial ID | Math Tutorial Title | Tutorial | Video
Tutorial | Revision
Notes | Revision
Questions |
|---|
| 7.3 | Standard Form | | | | |
| Lesson ID | Math Lesson Title | Lesson | Video
Lesson |
|---|
| 7.3.1 | The Meaning of Standard Form. | | |
| 7.3.2 | Writing Decimals in Standard and Decomposed Form | | |
| 7.3.3 | Addition and Subtraction with Numbers in Standard and Decomposed Form | | |
| 7.3.4 | Multiplication and Division of Numbers in Standard Form | | |
| 7.3.5 | Very Big and Very Small Numbers | | |
| 7.3.6 | Powers of Numbers Written in the Standard Form | | |
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- Continuing learning powers and roots - read our next math tutorial: Surds
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