I need help with these 3 questions!!!!!

Question

 
Simplify the following expression with rational exponents, putting the answer in simplest form: ((-3)^(1/5)) * ((-3)^(1/10))
 

(-3)^(3/10)

(-3)^(1/50)

3^(2/15)

-3

(-3)^(1/15)
 

Simplify the following expression with rational exponents, putting the answer in simplest form: (x^(1/3)) / (x^(1/6)). Note that this is a division problem.
 

x^(1/18)

x^(1/2)

x^(-1/3)

x^(1/6)

x^(-1/6)
 

Simplify the following expression with rational exponents, putting the answer in simplest form: ((x^(2/5)) * (y^(3/5)) ^ (1/6). Note that we are raising the entire product in parentheses to a power. Watch where the parentheses are, and carefully write this problem on a piece of paper so you can see what's being raised to what power.
 

(x^(17/30)) * (y^(23/30))

(x^(1/15)) * (y^(1/10))

(xy)^(1/6)

(x^(2/5)) * (y^(23/30))

(x^(3/30)) * (y^(4/30))

Answer 1

When multiplying two exponential numbers with the same base, you add exponents.

-3^1/5*-3^1/10 = -3^(1/5+1/10) = -3^2/10+1/10 = -3^3/10

When dividing, you subtract

x^1/3/x^1/6 = x^1/3-1/6 = x^1/6

When taking a power to a power (a "power tower"), you multiply the exponents

(x^2/5*y^3/5)^1/6 = x^2/5*1/6y^3/5*1/6 = x^1/15y^1/10

 

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