Express each of the following as a rational number of the form p/q, wh

1.	Express each of the following as a rational number of the form p/q, where p and q are integers and q ≠ 0:(i) 2-3(ii) (-4)-2(iii) 1/(3)-2(iv) (1/2)-5(v) \((\frac{2}{3})^{-2}\)
Answer» As (we know that a^-n= 1/an) (i) 2^-3 = 1/2³ = 1/2×2×2 = 1/8 As (we know that a^-n= 1/an) (ii) (-4)^-2 = 1/-4² = 1/-4×-4 = 1/16 As (we know that 1/a^-n= aⁿ) (iii) 1/(3)^-2 = 3² = 3×3 = 9 As (we know that a^-n= 1/an) (iv) (1/2)^-5 = 25 / 15 = 2×2×2×2×2 = 32 As (we know that a^-n= 1/an) (v) (2/3)^-2 = 3² / 2² = 3×3 / 2×2 = 9/4

Express each of the following as a rational number of the form p/q, where p and q are integers and q ≠ 0:(i) 2-3(ii) (-4)-2(iii) 1/(3)-2(iv) (1/2)-5(v) \((\frac{2}{3})^{-2}\)

Answer»

As (we know that a^-n= 1/an)

(i) 2^-3 = 1/2³ = 1/2×2×2

= 1/8

As (we know that a^-n= 1/an)

(ii) (-4)^-2 = 1/-4² = 1/-4×-4

= 1/16

As (we know that 1/a^-n= aⁿ)

(iii) 1/(3)^-2 = 3²

= 3×3

= 9

As (we know that a^-n= 1/an)

(iv) (1/2)^-5 = 25 / 15

= 2×2×2×2×2

= 32

As (we know that a^-n= 1/an)

(v) (2/3)^-2 = 3² / 2²

= 3×3 / 2×2

= 9/4

Simplify:(i) (4-1 × 3-1)2(ii) (5-1 ÷ 6-1)3(iii) (2-1 + 3-1)-1
Write each of the following in exponential form:(i) \((\frac{3}{2})^{-1}\times (\frac{3}{2})^{-1}\times (\frac{3}{2})^{-1}\times (\frac{3}{2})^{-1}\)(ii) \((\frac{2}{5})^{-2}\times (\frac{2}{5})^{-2}\times (\frac{2}{5})^{-2}\)
By what number should (-15)-1 be divided so that the quotient may be equal to (-5)-1 ?
By what number should \((-15)^{-1}\) be divided so that the quotient may be equal to \((-5)^{-1}\)?
By what number should (1/2)-1 be multiplied so that the product may be equal to (-4/7)-1 ?
Find x, if(i) \((\frac{1}{4})^{-4}\times (\frac{1}{4})^{-8}=(\frac{1}{4})^{-4x}\)(ii) \((\frac{-1}{2})^{-19}\div (\frac{-1}{2})^{8}=(\frac{-1}{2})^{-2x+1}\)(iii) \((\frac{3}{2})^{-3}\times (\frac{3}{2})^{5}=(\frac{3}{2})^{-2x+1}\)(iv) \((\frac{2}{5})^{-3}\times (\frac{2}{5})^{15}=(\frac{2}{5})^{2+3x}\)(v) \((\frac{5}{4})^{-x}\div (\frac{5}{4})^{-4}=(\frac{5}{4})^{5}\)(vi) \((\frac{8}{3})^{2x+1}\times (\frac{8}{3})^{5}=(\frac{8}{3})^{x+2}\)
By what number should \(5^{-1}\) be multiplied so that the product may be equal to \((-7)^{-1}\) ?
By what number should 5-1 be multiplied so that the product may be equal to (-7)-1 ?
Find x, if(i) (1/4)-4 × (1/4)-8 = (1/4)-4x(ii) (-1/2)-19 ÷ (-1/2)8 = (-1/2)-2x+1(iii) (3/2)-3 × (3/2)5 = (3/2)2x+1
By what number should \((\frac{5}{3})^{-2}\) be multiplied so that the product may be \((\frac{7}{3})^{-1}\)?