Question

By what number should minus 2 upon 3 raise to the power 3 be divided so that the quotient is 9 upon 8 raise to the power 2

Answer 1

Solution:

Let (-2/3)³ should be divided

by x get the quotient (9/8)²

=> (-2/3)³ /x = (9/8)²

=> (-2/3)³ × (8/9)² = x

=> (-2³/3³)×(2³/3²)² = x

=> (-2³/3³)×(2^6/3⁴) = x

=> (-2³×2^6)/(3³×3⁴) = x

=> (-2^9)/3^7 = x

Therefore,

Required number (x) = (-2^9)/3^7

••••

Answer 2

Answer:

- 512 / 2187

- 4(2/3)⁷

Step-by-step explanation:

By what number should minus 2 upon 3 raise to the power 3 be divided so that the quotient is 9 upon 8 raise to the power 2

Number given = ( -2/3)³

Let say the number by which it should be divided = x

Quotient = (9/8)²

=> Number given / x  = Quotient

=> x =  Number given / Quotient

=> x =  ( -2/3)³ / (9/8)²

( -2/3)³ = -8/27

(9/8)² = 81/64

=> x =   (-8/27) / (81/64)

=> x =  -(8 * 64 ) /(27 * 81)

=> x =  - 512 / 2187

=> x = - 2⁹/ 3⁷

=> x = - 2² *  2⁷ /3⁷

=> x = - 4(2/3)⁷