Originally Posted by
Jhevon ok. i assume you know the laws of exponents, and how to raise things to powers and add the powers when multiplying things of the same base, so let's not go into that. if you don't, look it up or see the thread that was suggested earlier.
now i'm going to walk you through question 2. don't just read what i did once and say you don't understand, re-read each sentence and each step, until you get it. if you are SURE that no matter how many times you read it you will not get it, then say so.
here goes. the question is:
12.5 m^2 = ? cm^2
since we want to go from m to cm, you look for the equation that i posted with 1 m = ? cm. when you find that, we're in business.
now i did post such an equation, it goes like this:
1 m = 10^2 cm
so, since 1 m is the same as 10^2 cm, it means that in the question, wherever i see 1m i can replace it with 10^2 cm, becuase they are the same thing, that's what being equal means.
so we have 12.5 m^2, since 1m = 10^2 cm
12.5 m^2 = 12.5 (10^2 cm)^2
see how i replaced the red text with the new red text, because they are the same thing. now all we have to do is simplify
now to raise something to a power to another power, we multiply the powers. that is, (x^m)^n = x^(m*n)
so (10^2)^2 = 10^(2*2) = 10^4
and (cm)^2 = cm^2
so we can just raise the 10^2 and cm to the second power as described above and keep them beside each other, which is another law of exponents.
that is, (x*y)^2 = x^2 * y^2
so, 12.5 (10^2 cm)^2 = 12.5 * (10^2)^2 cm^2
= 12.5 * 10^4 cm^2
= 1.25 x 10^1 * 10^4 cm^2 .........i changed 12.5 to scientific notation, i hope you know how to do that
now we have 10^1 * 10^4
a law of exponents says, that if we multiply the same base (in this case 10) we add the powers to get the new power, and raise the base to the new power.
so 10^1 * 10^4 = 10^(1 + 4) = 10^5
so, 1.25 x 10^1 * 10^4 cm^2 = 1.25 x 10^5 cm^2
so 12.5 m^2 = 1.25 x 10^5 cm^2
and we're done