Tetration

"something" - 3 "is" -8

Rename "something" "x". Realise the "is" means "is equal to" or "=".

x - 3 = -8    Add 3 to both sides:

x = - 8 + 3 = -5

Please rephrase the question to make it easier to understand?

I'm not sure I get it. Both Penn and Teller have sequences with positive integers, yet Teller's first term is the negative of Penn's first term. That sounds contradicting to me ...?

Yeah, the more experienced math helper and friend Melody, and me, interpreted the question differently. 

At any rate, please include paranthesis and/or multiplication symbols to make the question unambiguous. :)

$$z^{6x^{3}} / z^{4x^{5}}$$

In power towers like these, always solve from the "deepest level" first, in the notation, the highest level.

$$z^{216x^{3}} / z^{1024x^{5}}$$

Remember the formula:

a^b / a^c = a^{b - c}

We get:

$$z^{216x^{3}-1024x^{5}} = z^{x^{3}(216-1024x^{2})}= z^{8x^{3}(27-128x^{2})}$$

Did you want it expressed in some other way?

Would be cool if the puzzles themselves and their solutions were a bit distanced. Say, for instance, the questions were on one page, and their solution on another. :)

The specific puzzles could be numbered.

Alternatives:

2 * 2 + 2 = 6                         6/6 * 6 = 6

√3 * √3 + 3 = 6                     6√6 / √6 = 6

√(4 *4)+√4 = 6                     6/√6 *√6 = 6

4 * √4) - √4 = 6                    9 - (9 / √9) = 6

√√(4*4) + 4 = 6                    9 - √(√9 * √9) = 6

                                             9 - √√(9 * 9) = 6

1 foot ≈ 30.5 cm 

1 foot ≈ 0.305 m

1 foot² ≈ (0.305 m)² = 0.093025m² 

We see that this fraction equals 1:

$$\frac{1foot^{2}}{0.093025m^{2}}$$

So simply multiply (*) your square meters with this fraction, to get square feet.

To get from square feet to square meters, multiply by the multiplicative inverse of the (former) fraction, that is:

$$\frac{0.093025m^{2}}{1foot^{2}}$$

If it has an annual return of 7% it increases with 0.07 times the last year's investment. That means that the total amount of money one year later is 1.07 times the original amount of money.

After one year, the total amount of money is:

10⁴ * 1,07 = 1.07 * 10⁴

After two years, the total amount of money is:

10⁴ * 1,07 * 1.07 = 10⁴ * 1,07² = ...

After three years:

10⁴ * 1,07 * 1.07 * 1.07 = 10⁴ * 1,07³ = ...

Indeed, after x years, the total amount of money, T(x), has grown to:

T(x) = 10⁴ * 1.07^x 

Yeah, It's more than one way to skin a cat - and I'd prefer your solving strategy over mine :)