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Exponent power law with negative exponents

This math skill teaches how to simplify expressions involving powers raised to negative exponents. It explains the use of the exponent power law where one exponent is raised to another, and both the multiplication of exponents and the concept of the inverse of negative exponents are demonstrated.

Learn exponent power law with negative exponents

Teaching Transcript

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Let's simplify 5 the power of negative 2, raised to the power of 3

Remember that a number to a negative exponent is just the inverse, or 1 over, that exponent as a positive. So 5 to the negative 2, is 1 over 5 squared.

If we expand the exponent, we are multiplying fractions, which means we are multiplying top and bottom.

So our denominator, is 5 squared, times 5 squared, times 5 squared, or 5 to the power of 6

Which is 5 to the power of negative 6

Remember that the power law for exponents says that if an exponent is raised to another exponent, we can multiply them. Negative 2 times 3 is negative 6, our answer.

Skill Practice

Exponent power law with negative exponents

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