Algebra 2 Problems of the Day

The following problems were taken from the ALGEBRA II (Common Core) Regents Exam given on Friday, January 27, 2017.
Previous problems can be found here

Part 1

7. The expression

is equivalent to

(2) (see below)

You may do some of these steps in a different order. You might combine several of them.
I'm breaking it down as much as I can so more people can follow along.
Here is my process:

Resolve the division by subtracting the exponents: 2 - (1/3) = 1 2/3 or 5/3.
Next resolve the exponents: to find a power or a power, multiply the exponents, so (5/3)(-1/2) = (-5/6)
A negative exponent indicates the reciprocal: m^(-5/6) = (1 / m^5/6)
A fractional exponent indicates the nth root: see illustration above.

8. What is the inverse of the function y = log ₃ x?

(3) y = 3^x
Logs are the inverse of exponential functions.




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