geno3141

When you divide by a common fraction, multiply by teh reciprocal:

     2 ÷ (2/3)  =  2 x (3/2)  =  (2/1) x (3/2)  =  6/2  =  3

The digits 1, 2, 4, 5, 8, and 10 cannot be the denominator; all the others can.

If 1 is the denominator, then there is no decimal.

If 2 is the denominator, it terminates after one decimal place.

If 5 is the denominator, it terminates after one decimal place.

If 10 is the denominator, it terminates after one decimal place.

If 4 is the denominator, it terminates after two decimal places.   (4 = 2 x 2, each 2 creates one decimal place)

If 8 is the denominator, it terminates after three decimal places.  (8 = 2 x 2 x 2, each 2 creates one decimal place)

If you get into calculus, you will be shown infinite series that produce the digits of pi.

If you want to compare fractions by only looking at their numerators, their denominators must be equal.

x^-7   means    1 / (x^7)

An expression with a negative exponent can be replaced with "1 / (the expression with a positive exponent)"

[ 22 · a^5 ]² / [ 200a ]²

[ 22 · a^5 ]²   =  22² · (a^5)²  =  484a^10                        When squaring multiplied factors, square each one.

[ 200a ]²  =  200² · a²  =  40000a²

So: [ 22 · a^5 ]² / [ 200a ]²  =  ( 484a^10 ) x ( 40000a² )            When raising an exponent to an exponent,                                                                                                               multiply the exponents.

     =  [ 484 / 40000] x [ a^10 / a² ]                     

     =  (121/10000) x a^8

     =  121a^8 / 10000

This is a very complex problem, do you have any questions about it?

-3 1/3 - 3  =  -6 1/3

Writing  -6 1/3  as a common fraction:  -19/3         (Any questions about how to do this?)

-9(-19/3)  =  171 / 3  =  57

-20  =  -4x - 6x

Simplify  -4x - 6x  to get  -10x

-20  =  -10x

Divide both sides by  -10:

  2  =  x

Knowing the formula for g(x) does not help me find the value of h(x). 

Did you miscopy something?

Yes, because the only factors of 6 (beside 1 and 6) are 2 and 3. Neither √2 nor √3 can be simplified.