PLEASE HELP WITH THESE MATH PROBLEMS?!?!?!?!?!?!

Question

I don't understand how to solve these problems. Could you please provide a step by step process?

 

Thank you

 

1. 7-4m^(5/3)=-4089

 

2. 6^3n+1=1

 

3. 3^-n=(1/27)

Answer 1

1)  7 - 4m^5/3 = -4089

 

Subtract 7 from both sides:

 

-4m^5/3 = -4096

 

Divide both sides by -4:

 

m^5/3 = 1024

 

Take the 5th root of both sides

 

(m^5/3)^1/5 = (1024)^1/5

m^1/3 = 4

 

Cube both sides:

 

(m^1/3)³ = 4³

m = 64

 

2)  6³ⁿ⁺¹ = 1

 

Now 6⁰ = 1, so we must have:

 

3n+1 = 0

3n = -1

n = -1/3

 

3)  3^-n = 1/27

 

Now 3^-n = 1/3ⁿ and 1/27 = 1/3³; so:

 

1/3ⁿ = 1/3³

n = 3