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Published byBlaze Hutchinson Modified over 7 years ago

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Do Now: Solve for x in the following equation: Hint: and

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Aim: How can our knowledge of exponents help us simplify rational expressions?

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Yesterday: We noted that When we multiplied two powers with the same base, we added their exponents. Knowing that, posit a way to simplify the following:

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Quotient of Powers Property If one power divides another THAT HAS THE SAME BASE, then you can subtract their exponents –Numerator’s exponent minus denominator’s exponent In general,

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Examples:

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Consider the following situation What are two different ways we could rewrite this fraction? Are these two expressions equal to one another? Yes!!!!!!!!!!!! !!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!

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Negative Power Property A base with a negative exponent can be rewritten (with a positive exponent) as its multiplicative inverse IF THE BASE IS NOT ZERO!!! In general, Examples:

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A final property: Yesterday, we noted that Posit a way to simplify

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Power of a Quotient Property A quotient raised to a power can be simplified by distributing the exponent to both the numerator and denominator AS LONG AS THE DENOMINATOR IS NOT ZERO!!!!!!!!!!!!!!!!!!! In general, Example:

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Applying our properties to rational expressions… Simplify:

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