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Exponent power law composite base

Teaching Transcript

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

First, we can change 27 into 3 to the power of 3, so our bases are the same. Now, 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, 3 times 6.

And, similarly, on the right, we would have 3 raised to, 9 times our mystery variable

Since our bases are the same now, we know that 3 times 6 must equal 9 times our mystery variable.

Which we can solve quickly for an answer of 2

This math skill involves using the exponent power law to solve equations with compound bases. By expressing all terms with the same base and applying the law where exponents are multiplied when one exponent is raised to another, you can simplify the equation and solve for the unknown variable.

Skill Practice

Exponent power law problems with a compound base

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