MaTh QuEsTiOn!?

Question

i don't know how to figure this out:

Solve for y when y=180 x(times) .5 to the xth power when x equals -.5. Please also give me an easy to understand explanation. I'm only in 8th grade.

Answer 1

it is easier for us on the solving end if you use *(shift+8) for "x(times)" and ^(shift+6) for "to the power"

so a readable version of your equation looks like: y=180*.5^x
so put in -.5 or -1/2 for x: y=180*.5^(-1/2)
and solve with a calculator: 254.558

Explaination:
Exponents sould always be expressed as fractions. the top number of the fraction is the power and the bottom part is the root, therefore, .5^(1/2) is the same as the square root of .5^1.

Negative exponents are the same as positive exponents, but 1 divided by the number. .5^(-1) it the same as 1/.5

Answer 2

(180x(.5))^(-.5)
Well, 180x.5 = 90 (multiply it out)
so you have 90^(-.5)
Negative exponents mean they belong under a fraction, and fractional exponents (like .5 = (1/2)) mean they belong under a radical.
So this means
1/(sqrt (90)) = 1/(3 sqrt 10)
I see you're getting different answers here, that's because your question is a little hard to read and it can be read in different ways. Which one is right?
We've explained how to do it, and the explanations agree, even though we don't agree on how to read your question.
That is, negative exponents mean 1/ (the expression) and fractional exponents mean radicals. So N^(-.5) means 1/(N^(.5)) which means 1/(sqrt N).
N^(1/3) means cube root of N, N^(!/5) means fifth root of N, etc.
So take those explanations and try it yourself on the problem as it is given to you in your homework. Good luck!

Answer 3

something to the .5 power means the square root of it. something to the negative power means 1 over it. So the answer would be 180*1/(sqrt(.5))