Express each of the following rational numbers with a positive expon

1.	Express each of the following rational numbers with a positive exponent:(i) (3/4)-2(ii) (5/4)-3(iii) 43 × 4-9(iv) ((4/3)-3)-4(v) ((3/2)4)-2
Answer» i) (3/4)^-2 = (4/3)² (a/b)^-n = (b/a)ⁿ) (ii) (5/4)^-3 = (4/3)³ ((a/b)^-n = (b/a)ⁿ) (iii) 4³ × 4^-9 = (4)^3-9 (aⁿ × a^m = a^n+m) = 4^-6 (1/aⁿ = a^-n) = (1/4)⁶ (iv) ((4/3)^-3)^-4 = (4/3)¹² ((aⁿ)^m = a^nm) (v) ((3/2)⁴)^-2 = (3/2)^-8 ((aⁿ)^m = a^nm) = (2/3)⁸ (1/aⁿ = a^-n)

Express each of the following rational numbers with a positive exponent:(i) (3/4)-2(ii) (5/4)-3(iii) 43 × 4-9(iv) ((4/3)-3)-4(v) ((3/2)4)-2

Answer»

i) (3/4)^-2

= (4/3)² (a/b)^-n = (b/a)ⁿ)

(ii) (5/4)^-3

= (4/3)³ ((a/b)^-n = (b/a)ⁿ)

(iii) 4³ × 4^-9

= (4)^3-9 (aⁿ × a^m = a^n+m)

= 4^-6 (1/aⁿ = a^-n)

= (1/4)⁶

(iv) ((4/3)^-3)^-4

= (4/3)¹² ((aⁿ)^m = a^nm)

(v) ((3/2)⁴)^-2

= (3/2)^-8 ((aⁿ)^m = a^nm)

= (2/3)⁸ (1/aⁿ = a^-n)

Simplify:(i) (4-1 × 3-1)2(ii) (5-1 ÷ 6-1)3(iii) (2-1 + 3-1)-1
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