(KS3, Year 7)
The LessonPowers can be multiplied together. To multiply powers, add the exponents together.
This is a law of exponents.
How to Multiply PowersMultiplying powers is easy.
QuestionUse the law of exponents to multiply the powers below.
Check that the bases of the powers are the same. In our example, the bases are both 2.
Find the exponents of the powers
Find the exponent of the first power. In our example, the first power has an exponent of 2.
Find the exponent of the second power. In our example, the second power has an exponent of 3.
Add the exponents from Step 2 (2 and 3).
2 + 3 = 5
Make the answer from Step 3 (5) the exponent of the base of the powers that have been multiplied.
Answer:We have multiplied the powers together.
Understanding Multiplying PowersLet us look at the rule for multiplying powers:
- We are multiplying powers. 2m, 2n and 2m + n are powers.
- The base in each power is 2. This law of exponents only applies when the bases are the same.
- The exponents in each power are m, n and m + n. This law of exponents applies even when the exponents are different.
Lesson SlidesThe slider below shows another real example of how to multiply powers. Open the slider in a new tab
Why Does It Work?Consider the example below.
Each term is given by:
s Multiplying the two together gives:
This shows why the formula given works.
The Bases Must Be The SameThe law of exponents discussed here only works when the bases are the same. The multiplication below cannot be simplified, and must be left as it is:
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