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3 years ago

How would you write 6x6x6x6 asan exponential expression

Mathematics

2 answers:

agasfer [191]3 years ago

7 0

Basically, all you have to do is count how many 6 's you have and then write 6^4. Which is 6 to the fourth power.

faltersainse [42]3 years ago

7 0

Your answer would be 6 4. If you look at your problem, it has 4 sixes. The number of sixes, or other numbers, represent the exponent

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Evaluate 1^3 + 2^3 +3^3 +.......+ n^3

Molodets [167]

Notice that

$(n+1)^4-n^4=4n^3+6n^2+4n+1$

so that

$\displaystyle\sum_{i=1}^n((n+1)^4-n^4)=\sum_{i=1}^n(4i^3+6i^2+4i+1)$

We have

$\displaystyle\sum_{i=1}^n((i+1)^4-i^4)=(2^4-1^4)+(3^4-2^4)+(4^4-3^4)+\cdots+((n+1)^4-n^4)$

$\implies\displaystyle\sum_{i=1}^n((i+1)^4-i^4)=(n+1)^4-1$

so that

$\displaystyle(n+1)^4-1=\sum_{i=1}^n(4i^3+6i^2+4i+1)$

You might already know that

$\displaystyle\sum_{i=1}^n1=n$

$\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2$

$\displaystyle\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}6$

so from these formulas we get

$\displaystyle(n+1)^4-1=4\sum_{i=1}^ni^3+n(n+1)(2n+1)+2n(n+1)+n$

$\implies\displaystyle\sum_{i=1}^ni^3=\frac{(n+1)^4-1-n(n+1)(2n+1)-2n(n+1)-n}4$

$\implies\boxed{\displaystyle\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}4}$

If you don't know the formulas mentioned above:

The first one should be obvious; if you add $n$ copies of 1 together, you end up with $n$ .
The second one is easily derived: If $S=1+2+3+\cdots+n$ , then $S=n+(n-1)+(n-2)+\cdots+1$ , so that $2S=n(n+1)$ or $S=\dfrac{n(n+1)}2$ .
The third can be derived using a similar strategy to the one used here. Consider the expression $(n+1)^3-n^3=3n^2+3n+1$ , and so on.

7 0

3 years ago

cricket20 [7]

The answer is no solution because when you solve the equation

3(x+4)=3x+4

3x +12=3x +4
-3x -3x

You get an answer of 12=4 which is not true so there cannot be a solution to this equation

The answer is A no solution

8 0

2 years ago

What equation is y=4/5x+8 in standard form

Nadya [2.5K]

Answer:

4x−5y=−40 I think thats the answer

3 0

2 years ago

Please help with this

BabaBlast [244]

Slope: (y2-y1)/(x2-x1) = m
Find the slope, m, then pick a point, plug in the x, y, and m, and solve for b in the equation:
y = mx + b
That is your y-intercept.
Take out your x and y, plug in m and b, and that is your generic form for your line, t.

3 0

2 years ago

If nine people are in a room and every person shakes hands exactly once with each of the other people, how many handshakes will

emmasim [6.3K]

The total number of handshakes = 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 36

Answer: 36 handshakes

4 0

3 years ago