One
The power (-5) in the denominator brings the 5^5 up into the numerator. So the answer must be 5^5 >> 1. That makes A and B wrong.
5^5 is 3125. That makes C incorrect. There is only 1 answer left.
Two
Take the reciprocal of both sides of the equation. K^4 moves up into the numerator. That's how powers work.
k^4 = 1/(1/256) = (1/1) / ( 1/256) = 1/1 * 256/1 = (1*256) / (1*1) = 256
k^4 = 256 Take the 4th root of both sides.
fourth root (k^4) = 4th root of (256)
k = 4 or (believe it or not - 4) both work.
(-4)^4 = 256
Answer 4 or - 4
Three
10^6 >>> (much greater than) 1
That makes A and B incorrect. I hope you are allowed to use a calculator. You can do this with the calculator supplied with windows and most phones that do everything but make coffee for you after they wake you up.
10^6 = can be put into your calculator as
10
^ or y^x or x^y
6
=
1000000
Four
To get the power of 10 when the number is between 0 and 1 count the number of zeros and and 1. Make your answer minus. There are 5 zeros. So the power is 5 + 1 = 6. Make the six minus. - 6
1 * 10^-6 is the answer.
Five
Something * 10^4 is that number multiplied by 10000
2.45 * 10^4 = 2.45 * 10000 = 24500 which is C
