Question

Evaluate: 
`(16/81 )^(-3/4) xx (49/9)^(3/2) ÷ (343/216)^(2/3)`

Answer 1

`(16/81)^(-3/4) xx (49/9)^(3/2) ÷ (343/216)^(2/3)`

= `([ 2 xx 2 xx 2 xx 2]/[ 3 xx 3 xx 3 xx 3 ])^(-3/4) xx ([ 7 xx 7 ]/[ 3 xx 3 ])^(3/2) ÷ ([7 xx 7 xx 7]/[6 xx 6 xx 6])^(2/3)`

= `[(2/3)^4]^(-3/4) xx [(7/3)^2]^(3/2) ÷ [(7/6)^3]^(2/3)`

= `(2/3)^( 4 xx - 3/4 ) xx (7/3)^( 2 xx 3/2 ) ÷ (7/6)^( 3 xx 2/3 )`

= `(2/3)^(-3) xx (7/3)^3 ÷ (7/6)^2`

= `1/(2/3)^3 xx (7/3)^3 xx 1/(7/6)^2`

= `1/[2/3 xx 2/3 xx 2/3] xx 7/3 xx 7/3 xx 7/3 xx 1/[7/6 xx 7/6 ]`

= `[1 xx 3 xx 3 xx 3]/[ 2 xx 2 xx 2] xx 7/3 xx 7/3 xx 7/3 xx [ 1 xx 6 xx 6 ]/[ 7 xx 7 ]`

= `[ 7 xx 3 xx 3]/2`

= `63/2`

= 31.5