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2^5   = 2 x 2x 2 x 2 x 2  =   ??? .....I'll let you finish this one...

I assume this is....  (-2/3)*6+1

Multiply  -2/3 x 6, first =

-12/3  = -4

Now, add the 1  →  -4 + 1  = -3

78+n=1323

Subtract 78 from 1323.

n = 1,245

10767 / 15701 = about .6858 ....now....move the decimal two places to the right and add a percent sign = 68.58%

Order of operations:

1. Solve what's inside the paranthesis

2. Multiply (*) / divide (:)

3. Add (+) / subtract (-)

4p + 5 - 7p = -1

5 - 3p  = -1      EITHER: Use the formula: a - b = -(b - a)

3p - 5 = 1

3p = 6

p = 2

OR: 

5 - 3p  = -1    Move the five over to the right side:

- 3p = -6      Multiply (*) both sides with -1:

3p = 6        Divide both sides by two

p = 2

                                           200

                                          100 x 2

                                       50 x 2 x 2

                                    25 x 2 x 2 x 2

                                   5 x 5 x 2 x 2 x 2

And there's the tree.....I just threw in the trunk for free......!!!

$$2\frac{1}{2}/6$$

The general method 

Turn the mixed numerals into an improper fraction using this formula (can you see why it's true):

$$a\frac{b}{c}=\frac{ac+b}{c}$$

We get:

$$2\frac{1}{2}=\frac{2*2+1}{2}=\frac{5}{2}$$

Thus the whole expression gets:

$$\frac{5}{2}/6=\frac{5}{2*6}=\frac{5}{12}$$

The efficient method

Realise that 2 1/2 =2.5

We get: 2.5/6 = 5/12

5.972E24 kg

"Holistic'..."Pedagogic"......

Hey..I'm from Louisiana....don't you realize that, down here, we have to use a dictionary for words that contain 3 or more syllables???       (LOL!!!)

Thx, I try to find a good balance between efficient writing and holistic and pedagogic answers :) 

Indeed, I believe I learn some English and some math along the way.

I'm from Norway, you know :)

$$2 / 1\frac{5}{7}$$

First: Turn the mixed numbers into an improper fraction, use this formula (can you see why it's true?):

$$a\frac{b}{c}=\frac{ac + b}{c}$$

We get:

$$1\frac{5}{7}= \frac{1*7+5}{7}=\frac{12}{7}$$

To divide a number by a fraction is the same as to muliply the number by the multiplicative inverse of the fraction:

$$a/\frac{b}{c}= a*\frac{c}{b}$$

We get:

$$2 / \frac{12}{7}=2*\frac{7}{12}=\frac{14}{12}=\frac{7}{6}$$

Thanks Chris :)

LOL!!!....Anonymous......

Just hover your cursor over the "log" button...the "ln" button will magically appear....

This season, bold patterns are In, and pastels are Out.

The value of the car after 6 years is given by:

20000(.80)^6  = $5242.88  .... so, selling it for $4000 would be less than what it is worth at that time......

G = g₆₄     Where g₁ = 3↑↑↑↑3  and g_n = 3↑^g_n-1 3

Here I've used knuth's up-arrow notation, whice is used to indicate different levels of hyperoperations. 

Graham's number is so gigantic that even it's number of digits is more than a googleplex. Much, MUCH more indeed. 

In general, you need a calculator or pages of tables. You can work out or memorize the trig ratios for few special cases, 30°, 45°, etc., and can memorize a few trig identities to combine these, but those are the exceptions. Every student is advised to memorize the right-angled triangles that apply to these special cases so you can work out the ratios from basics.

3p2-7p-40  ... I usually use "trial and error " for these.....I think of two numbers that multiply to the first  coefficient and do the same for the last coefficient......then, I see if the middle co-efficient "falls out"

So we might try

(3p - 8)(p + 5)   nope....I see that I get a "+15p"...so...let's just reverse the signs

(3p + 8) (p - 5)   yep.....that's what we need...!!!

Your detailed answers are very good, Tetration....

Remember the formula:

C = pi*d 

Where C is the circumference, pi is the constant pi≈ 3.14 and d is the diameter of the circle.

Also remember that the diameter is twice the radius (witch makes sense when you think about it)

d = 2r 

The circunference of a circle is given  by  [ 2 * pi * r ]   where r is the radius....

You should be able to calculate it based on this....

Order of operations:

1. Solve what's inside the paranthesis

2. Multiply (*) / divide (:)

3. Add (+) / subtract (-)

3x + 2(x + 7) - 5 = 4(x + 3) - 3(x + 1)

3x + 2x +14 - 5 = 4x + 12 - 3x - 3   

5x + 9 = x + 9      You'd typically like to have the x'es on the lift side

                            Move the x to the left, and the nine on the left side over to the right side

4x = 0

x = 0 

We don't see anything, here..(???)