Simplify:

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

(i) (16) ^{-1/5 × 5/2}

= (16) ^-1/2

= (4²) ^-1/2 = (4)^-1

=

(ii) [(343)^-2]^1/3

= (343)^{-2 × 1/3}

= (7³) ^-2/3 = 7^-2

=

(iii) ()^1/3 = (1 / 10³) ^1/3

= = 0.1

(iv) (5²)^3/2 × (3⁵)^3/5 / (2⁴)^5/4 × (2³)^4/3

= (5)³ × (3)³ / (2)⁵ × (2)⁴

= =

(v) () ⁸ / () ¹³

= ( ^{– 5}

= 2 ^-5/2 / 5 ^-5

= 5⁵ / 2^5/2

=

(vi) 5^-7/2 × 7⁷ / 5⁷ × 7^-14 × 5⁵ × 7^-15/2 / 5 ^-15/2 × 7^25/2

= 7 ^{7 + 14} / 5^{7 + 7/2} × 5^{5 + 15/2} / 7^{25/2 + 15/2}

= 7¹ + 5² = 7 × 25 = 175