How to Find a Power of a Power in Algebra
Finding a Power of a Power in Algebra
We 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 Algebra
Finding a power of a power in algebra is easy.
Question
Use the law of exponents to find the power of the power below.
StepbyStep:
1
Find the exponents. In our example, the exponents are 2 and 3.
2
Multiply the exponents together.
2 × 3 = 6
3
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 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 (=):

Inside the brackets is a power, x^{2}. It consists of a base (x) raised to an exponent (2).
x^{2} means x is multiplied by itself 2 times:
x^{2} = x × x

This power becomes the base of another power, (x^{2})^{3}. Here, the base is x^{2} and the exponent is 3.
(x^{2})^{3} means x^{2} is multiplied by itself 3 times:
(x^{2})^{3} = x^{2} × x^{2} × x^{2}
By writing out this in full, we see that the left hand side is equal to x multiplied by itself 6 times: x^{6}.
x^{2} × x^{2} × x^{2} = (x × x) × (x × x) × (x × x)
x^{2} × x^{2} × x^{2} = x × x × x × x × x × x
x^{2} × x^{2} × x^{2} = x^{6}
Let us look at the right hand side of the equals sign (=):

x^{2 × 3} is a power. It consists of a base (x) raised to an exponent (2 × 3).
Clearly, x^{2 × 3} is equal to x^{6}. The left hand side of the equation equals the right hand side.