The LessonWe can find a power of a power. In this case, a power (with an exponent) is itself raised to an exponent. To find a power of a power, multiply the exponents together.
This is a law of exponents.
How to Find the Power of a Power in AlgebraFinding a power of a power in algebra is easy.
QuestionUse the law of exponents to find the power of the power below.
Find the exponents. In our example, the exponents are 2 and 3.
Multiply the exponents together.
2 × 3 = 6
Make the answer from Step 2 (6) the exponent of the base that has been raised to the exponent.
Answer:We have found the power of the power.
Understanding Powers of a Power in AlgebraLet us look at the rule for finding a power of a power, using the example above:
Firstly, let us look at what is to the left of the equals sign (=):
Inside the brackets is a power, x2. It consists of a base (x) raised to an exponent (2).
x2 means x is multiplied by itself 2 times:x2 = x × x
This power becomes the base of another power, (x2)3. Here, the base is x2 and the exponent is 3.
(x2)3 means x2 is multiplied by itself 3 times:(x2)3 = x2 × x2 × x2By writing out this in full, we see that the left hand side is equal to x multiplied by itself 6 times: x6.x2 × x2 × x2 = (x × x) × (x × x) × (x × x) x2 × x2 × x2 = x × x × x × x × x × x x2 × x2 × x2 = x6
- x2 × 3 is a power. It consists of a base (x) raised to an exponent (2 × 3). Clearly, x2 × 3 is equal to x6. The left hand side of the equation equals the right hand side.