If you think what raising to a power means:- n to power 2 is n multiplied by itself once, n to power 3 is n multiplied by itself twice . In general n to the power x = n multiplied by itself (x-1) times so n to the power 1 will be n multiplied by itself 0 times = n (not the same as multiplying by zero - just not multiplying n by anything). The big leap then is too see that n to the power zero is n multiplied by itself minus 1 times which is n divided by n =1. To see this more clearly picture the series created by any whole number raised to a power increasing by one incrementally from left to right. ...................n, nxn, nxnxn, nxnxnxn, nxnxnxnxn, .................... each new term is the old term multiplied by n. So if you go in the opposite direction each new term is the old term divided by n so:- n to power 2 divided by n =n to power 1 which is n so n to power 0 is n divided by n which is one, continuing on n to the power -1 is 1 divided by n (one nth) and n to the power -2 is 1 divided by n squared.
x to the n divided by x to the n is 1. By the law of powers x to the power n divided by x to the power n is x to the power (n minus n), ie x to the power zero. Things which are equal to the same thing are equal to each other. Therefore x to the power zero = 1. (Unless x = zero!)
It is 39*n+1 when divided by n, for any integer n.
The law of powers requires that xn divided by xm = x(n - m). Consider this when n = m: xn divided by xn = x(n - n), ie 1 = x0. x2 = x times x x1 = x times x divided by x ie x x0 = x divided by x = 1 x-1 = 1 divided by x = 1/x x-2 = 1/x divided by x ie 1/x2 etc
2n2 / n = 2n
1. All numbers to the zero power are 1. Take any number a^n we know that a^n/a^n=1 since anything divided by itself is 1. We also know the rule for division tells us a^n/a^n= a^(n-n)=a^0. so it is 1. 0^0 is usually defined as 1, but in some context people say it is indeterminate.
Anything to the power 0 is 1. Using the laws of powers to get to x to the power n-1 from x to the power n you divide by n; eg to get 4 squared (16) from 4 cubed (64) you divide 64 by 4. If you start with x to the power 1 and want x to the power zero, you divide by x. And x divided by x is 1.
It isn't. You're thinking of anything to the power zero. x0 = x(n - n) which equals xn divided by xn which equals 1.
n-1 = 1/n
1) One hundred and fifty divided by n; 2) n divided into one hundred and fifty.
For n not equal to -1, it is 1/(n+1)*xn+1 while for n = -1, it is ln(|x|), the logarithm to base e.
If it is to a (-) power then that is the same as saying it is 1 divided by 2 to the power of 1. 2 to the power of 1 is 2, and so 1 divided by 2 is 1/2 or 0.5.
This is represented as the algebraic expression xn/n or xn ÷ n.
Since n! is the product of all the numbers from 1 through n and (n+1)! is everything in n! multiplied by n+1, the quotient is n+1 ■
if we have two negative numbers, -n and -m and we divide them: (-n)/(-m) then we can rewrite the quotient as : (-1)*n/(-1)*m and... (-1)/(-1) * n/m we know that any number divided by itself is 1 by some rule: so = (-n)/(-m) = n/m which is positive
for expanding negative powers of a number you take 1 divided by the number to the positive power and expand. For example 2 to the -1 power is 1 divided by 2 to the + 1 power = 1/2 2 to the -3 power is 1 divided by 2 tot he + 3 power = 1/8 this is called inverse
You can write that in several different ways: n/8 n -- 8 1 -- n 8
You can think of this problem in two ways. First, as the more general question "What is N divided by N?" This makes the answer, 1, obvious. Second, you can work through it algebraically: (1/3)/(1/3) = N 1/3 = N/3 N = 1
7 to the tenth power divided by 7 to the ninth power = 1
1proof:n**3 * n**-3 = n**0n**3 = n*n*nn**-3 = 1/n * 1/n * 1/n1/n * 1/n * 1/n * n * n * n= n*n*n/(n*n*n) = 1Any number to the zero power = 1 .Any number to the ' 1 ' power = itself .Also:ex. 3^0 = 1but this is also the same value as :5^0 = 1Hence 3^0 = 5^0 = n^0 = 1If you had 3^2 / 3^2 the result is 1 since any value divided by itself it 1.Hence the base (here it's 3) and the exponent (here it's 2) is essentially eliminated and the result is just 1 as it would be for any other base and exponent. Mathematically, in an expression form you can eliminate (set to 0) the exponent by subtracting the exponents:3^2 / 3^2 = 1 = 3^(2-2) = 3^0 = 1 = n^0X^0=1How about this:If you had 5^2 / 5^2 , it equal 1 since any number divided by that same value is one. Therefore there is no power of 5 left since 5^1 would be 5. It is as if you subracted the exponents: 5^(2-2) = 5^0. This is valid because if you had something like:5^2 / 5^1 = 5^(2-1) = 5^125 / 5 = 5 = 5^1
(4/8)/(n^3)...4/8 reduces to 1/2 so the problem reduces to (1/2)/(n^3)...Which written in simple terms is 1/n^3. Actually I made a typo the answer is 1/(2n^3) Sorry about that.
Properties of Division: n/n =1, If n ≠ 0. Any number other than zero divided by itself is one.
n2 + n = n(n + 1)
That would be 1/8n.