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How is the power of power property rule and the power of a product property rule different?
(xa)b = xa*b = xab (xy)a = xaya
Is a squared plus b squared the same as a plus b squared?
No. If you expand (a + b)2 you get a2 + 2ab + b2. This is not equal to a2 + b2
Can the square root of a and square root of b equal the square root of A plus B?
sqrt(a)+sqrt(b) is different from sqrt(a+b) unless a=0 and/or b=0. *sqrt=square root of
How do you find the constant rate of change on graph?
You measure the change in the vertical direction (rise) per unit change in the horizontal direction (run). The rate of change is constant between A and B if AB is a straight line. Take any two points, A = (xa, ya) and B = (xb, yb) then the average rate of change, between A and B = (yb- ya)/(xb- xa).
When a squared plus b squared equals c squared what is the square root of the square root of the square root of a squared squared squared plus b squared squared squared?
Since a squared plus b squared equals c squared, that is the same as c equals the square root of a squared plus b squared. This can be taken into squaring and square roots to infinity and still equal c, as long as there is the same number of squaring and square roots in the problem. Since this question asks for a and b squared three times, and also three square roots of a and b both, they equal c. Basically, they cancel each other out.
How do you find the answer of a number having its power as a fraction?
Suppose you have the expression Xa/b. Xa/b is equal to b√(Xa) that is, the bth root of (X to the power a). Equivalently, it is (b√X)a, that is (the bth root of X), raised to the power a.
Why exponent 0 is equal to 1 to this problem 1x2 exponent 0 is equals 1?
x to the power a divided by x to the power b = x to the power (a - b), ie xa/xb = xa-b. When a = b, xa/xb = 1 and a - b = 0 so xa-b = x0. Rearranging gives x0 = 1. This is true for ALL non-zero values of x.
How do you find the gradient of two points?
If A = (xa, ya) and B = (xb, yb) and xa is not equal to xb, then gradient of AB = (ya - yb)/(xb - xb).If xa = xb then the gradient is undefined.
Why is 10 power 0 equal to 1?
Any number to the power zero is equal to one. That can be derived from the following index law: xa*xb = xa+b (x not zero) Now let b = 0 so that the above becomes xa*x0 = xa+0 so xa*x0 = xa (since a+0 = a) That is, any number multiplied by x0 is the number itself. That can be true only if x0 is the multiplicative identity, that is, only if x0 = 1.
Why a number to the zero power is always equal to 1?
It is a consequence of the definition of the index laws. xa * xb = xa+b If you put b = 0 in the above equation, then you get xa * x0 = xa+0 But a+0 = a so that the right hand side becomes xa Thus the equation now reads xa * x0 = xa For that to be true for all x, x0 must be the identity element for multiplication. That is x0 = 1 for all x.
Why any number raised to power zero is 1?
This derives from one of the laws of indices which states that, for any x (not = 0), xa * xb = xa+b Put b = 0 Then xa * x0 = xa+0 = xa (because a + 0 = a) But that means that x0 is the multiplicative identity. And since that is unique, and equal to 1, x0 = 1. This is true for all x. Put
Why the exponent rule of zero equals one?
The exponent rule for multiplication is xa * xb = xa+b Now, if you put b = 0, then a+b = a so that the above reads: xa * x0 = xa which only works if x0 = 1.
What does b plus a plus b-a equal?
b + a + b - a = 2b
Which is bigger 4 to the power of 3 squared or 2 to the power of three to the power of 4?
Neither. They are equal.(43)2 is the same as 46 = 4096 ...remember (xa)b = xa*b(23)4 is the same as 212 = 4096
What property allows you to rewrite xa xb as xa b?
associative
What is x to the power of a plus 1 times x to the power of a plus 1?
The question is ambiguous: xa+1 * xa+1 = x2(a+1) or (xa + 1)(xa + 1) = x2a + 2xa + 1
Why is 6 raised to the 0 power 1?
Any number raised to the power 0 is 1. This follow from the law of multiplications of power: xa * xb = xa+b Now, if you put b = 0, you get xa + x0 = xa+0 and since a+0 = a, the right hand side is xa. So you have xa * x0 = xa and using the property of the multiplicative identity, xa = 1.
