HELP!! me with my math!?

Question

ok for math i have this problem that is like this : 2 to the 5th power and there is another one that is (-2) to the 5th power... wat is the difference? for the anwser key one of them is negative but how? (o ya im in 7th grade so dont tlk like a professor)

Answer 1

2 to the 5th power = 2*2*2*2*2 which basically means 2*2 = 4 *2 =8 *2 =16 *2 = 32
(-2) to the 5th power = -2*-2*-2*-2*-2 which basically means -2*-2 =4 *-2 =-8 *-2 =16 *-2 = -32.

Answer 2

Quick rule of thumb: Even exponents will always yield positive numbers. Odd exponents will give you back the sign of the original number.

Now, how does this work? Let's examine your 2 and -2.
2 to the 2nd power = 2 * 2 = 4
(-2) to the 2nd power = (-2) * (-2) = 4
When you multiply two negatives, you get a positive.

Also, you can write power with a ^ symbol so 2 to the 2nd power is 2^2.

A positive number taken to any power will yield a positive number. This is a property with real numbers. A positive multiplied by a positive will yield a positive. So, 2^5, 2^80, and 2^9247297494827942 will all give a positive number.

Now, negative numbers are different. When you multiply a negative and a positive, you get a negative. When you multiply two negatives, you get a positive. This is handy to know. So, expand your (-2)^5.

(-2)^2 = (-2) * (-2) = 4
(-2)^3 = (-2) * (-2) * (-2) = 4 * (-2) = -8
(-2)^4 = (-2) * (-2) * (-2) * (-2) = (-8) * (-2) = 16
(-2)^5 = (-2) * (-2) * (-2) * (-2) * (-2) = 16 * (-2) = -32

Note how it builds on itself. (-2)^5 = (-2)^4 * (-2). So, if you know the earlier powers, then you can rely on that. Ultimately, it goes back to the rule of thumb I first posted: Even powers yield positive values while odd powers yield the same sign as the original number.

BTW, you'll note that I wrote (-2)^5. This is important to note. It means taking -2 to the fifth power. If I wrote it as - 2^5, then that means taking 2 to the fifth power and negating it. Sure, in this instance, they are both equal, but you can see that (-2)^4 does not equal - 2^4.

Answer 3

I hope this is right:
2 to the 5th power is 2x2x2x2x2 = 32
If it is -2 to the 5th power, the answer would be negative because it is not "protected" by parenthesis. so it would be 2x2x2x2x2 = 32 so the answer would be -32.
However if the -2 is in parenthesis (-2) it would be the same as saying (-2)(-2)(-2)(-2)(-2) but the answer would still be -32. Because two negatives multiplied = positive then a positive and a negative multipled = a negative number. Hope this helps.

Answer 4

Well, when you multiply 2 negatives, you get a positive, now, -2 ^5 = -2 x -2 x-2 x-2 x-2, now, theres 5 negative signs, take out 4 (since they will cancel each other out as 2 negatives equal a positive, and you're left with 1 negative, which makes the answer negative. However, if the problem is like this -(2)^5, then it's negative no matter what, as you leave the negative out of the equation. i.e. -(3)^4 = -(3x3x3x3). Multiply inside first, then add the negative when you're done :)

The question you have. (-2)^5, which means the first one I said, again, just cancel out negatives in groups of 2, if theres 6 negatives, the answer will be positive, if there's 9, it will be negative. As long as the negative sign is inside the parenthesis, just use this method. If it's outside, the answer is always negative.

Answer 5

ok im in 8th grade so yea

ok when its a negative it would be -2 * -2 * -2 * -2 * -2 =
it would be (-2)(-2) = 4(-2) = -8(-2)= 16(-2) = so it would be -32

positive 2 to the fith power would be
2 *2 *2 *2 * 2 = 32


see one is negative and one is positive

because the power of the number(5) is odd
so when a negative is with an odd number it reamins negative
positive will always remain positive


i hope i helped

Answer 6

2 to the 5th power means
2 x 2 x 2 x 2 x 2
= 4 x 4 x 2
= 16 x 2
= 32

BUT -2 to the 5th power means
-2 x -2 x -2 x -2 x -2
= 4 x 4 x -2
= 16 x -2
= -32

So, you can see there's a difference.

Answer 7

2 to the 5th power = 32

-2 to the 5th power = -32

The 5 in the 5th power is the amount of times you're supposed to multiply the 2.

2 times 2 times 2 times 2 times 2 = 32.

Answer 8

2^5 is 32, (-2)^5 is -32. Because: The power that -2 is being raised to is odd. Negative quantities inside a parenthesis raised to an even power are positive, raised to an odd power are Negative. IE (-)(-)=positve (-)(-)(-)=negative. It is an alternating series

Answer 9

2 to the 5th is
2x2x2x2x2
\ / \ /
4 x 4 x 2
16x2
32
(-2)to the 5th is
-2x-2x-2x-2x-2
\ / \ /
4 x 4 x -2
16 x-2
-32

Answer 10

basically if it is a negative number to the power of an odd number then the answer is going to be negative
if it is a negative number to the power of an even number then the answer is going to be positive