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.