If 27^x =, find x.

Simplify:

(i) (16^-1/5)^5/2 (ii) (iii) (0.001)^1/3 (iv) (v) (vi)

Prove that:

(i)

(ii) 9^3/2 -3× 5⁰ - = 15

(iii) -3×8^2/3 ×4⁰+

(iv) = 10

(v) + (0.01)^-1/2 – (27)^2/3 =

(vi)

(vii)

(viii) = 28

(ix)

Find the values of x in each of the following:

(i) 2^5x÷ 2^x =

(ii) (2³)⁴ = (2²)^x

(iii)

(iv) 5^x-2 × 3^2x-3 = 135

(v) 2^x-5 × 5^x-4 = 5

(vi) 2^x-7 × 5^x-4 = 1250

Write (625)^-1/4 in decimal form.