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

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

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:

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,

Examples:

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

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:

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

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:

Applying our properties to rational expressions… Simplify: