My Math Forum Test in a few hours! (fractional exponents)

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 January 12th, 2012, 09:52 AM #1 Member   Joined: Dec 2011 Posts: 44 Thanks: 0 Test in a few hours! (fractional exponents) Going over some concepts I'm not fully understanding. This one deals with fractional exponents. Evaluate each, if possible: 1.) -(-32)^3/5 2.) 4th root of ((30pq)^7) -->(the 7 is inside the radical) For 1.), I'm not sure if there is a simple way to reduce it. I tried figuring out and kept running into Newton's Method, which seems kind of relevant, but there has to be an easier way to simplify this. I started doing it this way, which is really long and easy to make a mistake, but it's the only way I can visualize it right now: -5th root of ((-32)^3) I factored the large number and ended up with (2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2) so 2^11, since we're taking the 5th root, I removed 10 of the 2's in the radical, and I was left with: 4 times the 5th root (2). I'm probably way off, I don't know. I can't figure an easier way to do this. For the 2nd problem, I have no idea. It's just too hard for me to simplify doing it this way, if that last way was even correct.
 January 12th, 2012, 10:06 AM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs Re: Test in a few hours! (fractional exponents) 1.) $-$$-32$$^{\frac{3}{5}}=-$$(-2)^5$$^{\frac{3}{5}}=-(-2)^3=-(-1)^3(2)^3=2^3=8$ 2.) $\sqrt[4]{$$30pq$$^7}=\sqrt[4]{$$30pq$$^4\cdot$$30pq$$^3}=30pq\sqrt[4]{$$30pq$$^3}$
 January 12th, 2012, 10:12 AM #3 Member   Joined: Dec 2011 Posts: 44 Thanks: 0 Re: Test in a few hours! (fractional exponents) GOT IT! Thank you!!!

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