How to Find a Power of a Power in Algebra (Mathematics Lesson)
Finding a Power of a Power in Algebra
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 Algebra
Finding a power of a power in algebra is easy.
An Example Question
Use 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.
Make the answer from Step 2 (6) the exponent of the base that has been raised to the exponent.
We have found the power of the power.
Understanding Powers of a Power in Algebra
Let 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 (=):
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 × x2
By 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
Let us look at the right hand side of the equals sign (=):
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.
A Real Example of How to Find a Power of a Power in Algebra
The slider below shows another real example of how to find a power of a power in algebra.