solve with rational exponents

Question

(x-3)^3/2 =64

 

 

 

 

second question:

(x²-x-51)^3/4-4=23

Answer 1

Maria has the right solutions, but allow me to show you the break down. 

 

 

1)

 

(x - 3)^3/2 = 64

 

 

We want (x - 3) to have a power of 1.  To do that, we raise both sides of the equation by 2/3.   The exponents  multiplied together gives us 1.

 

 

[(x - 3)^3/2]^2/3 = 64^2/3

 

x - 3 = 64^2/3

 

 

We can convert the fraction exponents to radicals.  Using the rules of radicals,

 

x - 3 = ³√(64²)

 

 

Next, we can break up the radicals on the right side of equation.

 

x - 3 = ³√(64) * ³√(64)

 

x - 3 = 4 * 4

 

x - 3 = 16

 

x = 19

 

 

Do the same process for the second question.

Answer 2

(x-3)^3/2 =64

x-3 = 64^2/3

x-3 = 16

x = 16 + 3

x = 19

 

 

(x^2-x-51)^(3/4) - 4 = 23

(x^2-x-51)^(3/4) = 27

(x^2-x-51) = 27^4/3

x^2-x-51 = 81

x^2-x-132 = 0                  -12 x 11 = -132     and     -12 + 11 = -1

(x-12)(x+11) = 0

x = 12

x = -11