Tetration

x² + 5x = 0

x(x + 5) = 0

x = 0 v x + 5 = 0

x = 0 v x = -5

Where v is the inclusive disjunction. (basically means "or")

Percent means "per hundred": 12,5% = 12,5/100 = 0,125.

In order to subtract (-) one fraction from another, you need to find a common denominator (bottom). This is done by multiplying (*) the numerator and the denominator in a fraction by the same number:

$$\frac{3}{4}-\frac{5}{6}=\frac{3*3}{4*3}-\frac{5*2}{6*2}=\frac{9}{12}-\frac{10}{12}=-\frac{1}{12}$$

So we get:

$$\frac{0,125}{(-1/12)^{2}}$$

When to fractions are multiplied together, one multiplies the numerator by numerator and denominator by denominator:

$$(-\frac{1}{12})^{2}=(\frac{1}{12})^{2}=\frac{1}{144}$$

So we get:

$$\frac{0,125}{1/144}$$

Multiply the numerator and the denominator by 144:

$$\frac{0,125*144}{1}= 0,125*144$$

Pi is a mathematical constant. It's value is approximaly 3,14. 

It is the ratio between a circle's circumference to it's diameter:

$$Pi = \frac{C}{d}$$

Pi is an irrational number, that is, it cannot be represented as a ratio of integers. This also implies that pi has infinitely many decimals, and isn't a repeating decimal. In fact a better approximaton for pi is: 3.141592653589793...

$$\frac{8}{1/3}$$

To divide a number by a fraction in which the numerator (top) is one, is the same as to multiply the number by the denominator:

$$\frac{a}{1/b} = ab$$

So in our case:

$$\frac{8}{1/3} = 8*3 = 24$$

*** Thx :-) ***

[n²(n²)]

The outer paranthesis (brackets) are unnecessary:

 n²(n²)

Remember that:

n^a * n^b = n^{a +b}

So we get:

n²(n²) = n⁴

$$\frac{5}{6}*30$$

Let's first look at the general case:

$$\frac{a}{b}*k$$

To calculate this, simply multiply the number (in this case k), with the numerator (top, in this case a), and divide the product with the denominator (bottom, in this case b):

$$\frac{a}{b}*k = \frac{a*k}{b}$$

So in our case, we get:

$$\frac{5}{6}*30 = \frac{5*30}{6}=\frac{150}{6}= 25$$

(-3)³ = (-3)(-3)(-3) = 9(-3) = -27

In general we have that (-X)^k = X^k when k is an even number, and (-X)^k = -(X^k) when k is an odd number. 

Remember that -(-x) = +x = x

-11 - (-11) = -11 + 11 = 0

Welcome back :)