another math question ( grade 7)?

Question

ok, this question is getting me a little confussed. im not looking for the answer though. just how to get there
heres the question

Areas of land are measured in hectares. one hectare is the area of a square with side length 10 to the power of 2 meters. Express the number of square metres in a hectare as a power

thanks in advance :)

Answer 1

The question gives you the answer. 10^2.

Answer 2

Okay, so basically it just wants you to find the area of the square. Since it tells you that one side is 10^2 and to get the area you need length x width you simply multiply 10^2 by 10^2.

But, since it wants the answer in a powered notation (written to the power of somethin') Take the side and put is to the power of two because two things multipiled together can be sait to that power of two.
ie (10^2)^2
All you need to do then is to multiply the exponent together to get the answer...
= 10^(2x2)
= 10 ^ (4)
= 10^4
is how big a hectare is with a side of 10^2.... I know you didn't want the answer but that's only way I could explain it. Hope it helps a little

Answer 3

10^4 m²/hectare

Note that a square with length 10² meters (i.e. 100 meters) will have an area of (10²)² meters. You can then use the exponent laws to simplify this without multiplying it out: (a^b)^c=a^(b*c). To see why this is true, consider that a^b is:

(a*a*a*a...*a) (b times)

So (a^b)^c is:

(a*a*a*a...*a) * (a*a*a*a...*a) * (a*a*a*a...*a) * (a*a*a*a...*a)... (a*a*a*a...*a) (c times)

Since multiplication is associative, the parentheses are irrelevant, so this is just the product of some number of a's - i.e. a to some power. But how many a's? There are c groups, each containing b a's each, so this gives a total of b*c a's, thus you have a^(b*c).

Please excuse the use of apostrophes in the plural of a: I know it is technically incorrect, but the proper form looks too much like the word "as" and thus would be too confusing.

Answer 4

Hi Madame,

The problem says one hectare is the area of a square with side length 10^2 m. So picture a square, sized 100m by 100m, that's your hectare.

So the area of the hectare is 100m * 100m = 10,000 m^2

Since your problem said to put the answer in terms of powers, maybe if you did the problem like this:

10^2 m * 10^2 m = 10^4 m^2

That might be what you're looking for.

HTH! :-)

Answer 5

The question gives you the answer. Forget about Hectares, whatever. It doesn't matter what they are. How would you find the area of the square?

Answer 6

1/10^2 hectares

Answer 7

Each side is 100 meters long, or 10^2 m.
Area of a square=side^2. 100^2=100*100=10,000 or 10^4
Ans: 10^4 m^2

Answer 8

AUG has it right anyway just thought I'd answer this for the two points and then bag out the professor for not being able to understand the question or spell college must be an art professor or something

Answer 9

a power is Ex. 10^2 (ten squared)
it is written 10 with a little number above it to the right (2)
it means 10x10 just as 10^3 would be 10x10x10

Answer 10

Im a collage proffesor and i dont know what the heck your talking about!!!!!!!!!!!!!!!!!!!@@@@@