Thread: Exponents and Equations

I have a bunch of questions here. Some I am unsure about the answer, some I just can't do.

1. Simplify (2a⁷ x 50a³)^-1/2
For this one I would assume you do inside the brackets first, and then do the power of negative 1/2, so: (100a¹⁰)^-1/2... THIS is the answer I get: 0.1a^-5
Is that right?

2. Write log 8 + log 16 in terms of log 2.
I ended up going: log 2³ + log 2⁴, and then 3 log 2 + 4 log 2, and then 7 log 2, and then log 2⁷. I'm not sure if I should go back a step and the answer is 7 log 2

3. Simplify (x² + 3x - 10)(x + 5)^-1 this one I can't do because I don't know whether to expand the brackets first, or what to do with the -1 power!!!

Please help.

1. That's correct.
2. It's correct in my opinion.
3. , can you factorize ?

I'm going to put my two cents in here. For problem 1 you probably should give the answer as 1/10 not 0.1. (Math at this level isn't usually expressed in digits.) For problem 2 the problem statement is given as logs so your answer probably be in logs as well. (So pick the 7 log 2.)

-Dan

Aha! For the last one I thought about making the exponent positive by putting a 1 on top of that last bracket... but your answer should have been obvious to me!! D'oh. Thanks to everyone who replied to this thread.