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Exponent power law problems

Exponent power law problems with the same base

This math skill teaches how to solve exponent power law problems with the same base. It explains that when an exponent is raised to another exponent, the operation is equivalent to multiplying these two exponents, given a common base. With identical bases, the exponents on both sides of an equation must be equal, which allows us to solve for any unknowns.

Learn exponent power law problems

Teaching Transcript

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Let's use the exponent power law to solve for the missing variable

The power law tells us that an exponent, raised to another exponent, is equal to the base raised to those exponents multiplied together. So, on the left, we would have 3 raised to, 4 times 6.

And, similarly, on the right, we would have 3 raised to, 3 times our mystery variable

Let's write the exponents in these forms, so we can start to see a way to solve it. Notice that the bases are the same

With identical bases, we know that the exponents must be identical, so 4 times 6 equals 3 times our mystery variable

Which we can solve quickly, and our answer is 8

Skill Practice

Exponent power law problems with the same base

Test your understanding of exponent power law problems by practicing it! Work through the below exercises to use it in practice.