Hi there. In this math education post, I talk about the algebra topic of powers to a power. This topic is normally a part of high school mathematics (grade 9).
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Before getting into learning about power to a power, it is best to review exponent laws when it comes to multiplying monomials.
Given two monomials such as 10x and
Think of
Consider a monomial such as 5x but raised to the power of 2. This would like
Let's go back to the definition of an exponent and apply exponent laws.
Having x-squared to the power of three gives x to the power of 6. The simpler way is to multiply the exponents of 2 and 3 to obtain the new exponent of 6.
The general formula given a base, exponent and a second exponent would be:
where p and q are (usually) integers.
A More Complex Example
So far we dealt with a single variable with a coefficient of 1. What if we have another variable and a number other than 1 in front? Let's take a look at
The outside exponent of 5 is applied to the 2,
In general, the formula would be:
where a, b, c are different variables and q is an integer exponent.
Try out these practice problems for better understanding and increasing algebra speed.
Thank you for reading.
