What is the difference, if there is any, between -xsquare and (-x)square?Use numerical example use this diff.?

Question

2. Explain how x to the power of m x to the power of n is equal to x to the power of m+n. Show how this is true using the meaning of exponents and multiplication. Use numerical examples to show it is true.

Answer 1

Well your first question "What is the difference, if there is any, between -xsquare and (-x)square?Use numerical example use this diff.?"

The difference is when the negative sign is in the parenthases and you square it it becomes a positive number and when there are no parenthases the answer is negative.
(-x)^2 = x^2 which is not equal to -x^2

For (-x)^2:
Since the negative sign is inside it becomes positive
(-5)^2 = 25

For -x^2:
Since only the x is squared the answer remains negative
-5^2 = -25

As far as (x^m)(x^n) = x^(m+n):

Example

(2^3)(2^5) = 2^(3+5) = 2^8 = 256

Well if you calculate 2^3 and 2^5 seperately you get
8*32 = 256

The reason this is true is because you are just adding up the number of times you are multiplying the number to itself.

2^3 = 2*2*2 That is 3 twos
2^5 = 2*2*2*2*2 That is 5 twos
(2^3)(2^5) = (2*2*2)*(2*2*2*2*2) = 2^8 That is 5+3 twos

Answer 2

1. -xsquared and (-x)squared gives different results, the latter giving a positive answer.

for example -5squared = - (5 x 5) = -25
however (-5)squared is -5 x -5 = +25

2. let X be 3.

3 to the power 1 x 3 to power of 2 = 3 to the power 3(1+2)

3 x (3 x 3) = 3 x 3 x 3
27 = 27

Answer 3

-xsquare will result in a negative while (-x)square will result in a positive. The difference is in the notation. In the first problem the negative is not included with the x while it is in the second. Here is an example: - 2squared = - 4, (-2) squared = 4.

Answer 4

Given:
y = -x^2 and h= (-x)^2 <=>
y = -x^2 and h= (-1)^2*x^2 <=>
y = -x^2 and h=x^2
hence: y = -h It’s obviously that
-x^2 & (-x)^2 has same numeric value
but opposite sign.
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Numeric example x= 13 =>
-x^2= -13^= - 169 & x^2= 13^2= 169
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Prove of x^n*x^m=x^(n+m)
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x^n= x*x*……...x & x^m=x*x*…………x =>
…….← n times →……←.. m times..→

x^n*x^m= (x*x*……...x)*( x*x*…………x) <=>
………….← n times →← m times .→

x^n*x^m= x*x……………………………..x <=>
………….←…… n + m times……......→

#) x^n*x^m=x^(n+m) Qed.
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Numerical example:
x= 2, n=4, m=5 =>
x^4=2^4= 16 & x^5 =2^5=32 => x^4*x^5=16*32=512
By use of formula #)
x^4*x^5=x^(4+5)=x^(9) & x=2 => 2^9=512
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Answer 5

-x^2 is negative. For example - (2*2)=-4
(-x)^2 is positive. For example (-2)(-2)=+4

Answer 6

No difference. (-x) squared = (-x)*(-x) = (-1*x)*(-1*x) = (-1)*(-1)*x*x = 1*x*x = x*x = x squared.

The same argument can show that (-x) to any EVEN power equals x to the same power. Put that in your homework too and you'll get an A.

Answer 7

1. No diff.
2. consider (x = 2, m =2, n= 3)
case 1: 2^2*2^3 = 4 * 8 =32----(1)

case 2: 2^5 = 32 ------(2)

From (1) and (2) 2^2* 2^3 = 2^5(2+3 = 5 i.e.
x^m*x^n = x^m+n)

Answer 8

no difference since any negative number multiplied by another negative number = a positive, they are both parabolic functions.