Simplify Leave your answers without negative exponents and i

Simplify. Leave your answers without negative exponents and in radical form or rational exponent form.

a) 64^2/3 = (8^2)^2/3 = 8^4/3

b) (3^-1/4)^-1 = 3^(-1*-1)/4^-1 = 3^1/4^-1

Now 3/4^-1 = 3*4^1 = 12

c) (sqrt8)^-2 = (8^1/2)^-2

= 8^(1/2*-2) = 8^-1 = 1/8

d) e^x*e^x = e^(x+x) = e^2x

e) (5x^0)/sqrt(5)

now x^0 =1

So, 5/sqrt5 ; rationalise denominator:

5sqrt5/sqrt5*sqrt5 = 5sqrt5/5 = sqrt5

f) sqrtx* (27x)^1/3

now 27= 3^3

So, sqrtx* (3^3)^1/3*(x^1/3) = x^(1/2+1/3)*3

= 3x^5/6