Question

Jim's work evaluating 2 (three-fifths) cubed is shown below. 2 (three-fifths) cubed = 2 (StartFraction 3 cubed Over 5 EndFraction) = 2 (StartFraction 3 times 3 times 3 Over 5 EndFraction) = 2 (StartFraction 27 Over 5 EndFraction) = StartFraction 54 Over 5 EndFraction Which statement best describe Jim's first error?

Answer 1

`2((3)/(5)) ^(3)=2((3^3)/(5^3))` and not
`2((3)/(5)) ^(3)=2((3^3)/(5))`

Explanation:

Jim's work evaluating
`2((3)/(5)) ^(3)` is shown:

`2((3)/(5)) ^(3)=2((3^3)/(5))=2((3X3X3)/(5))=2((27)/(5))=(54)/(5)`

If you look at the Second step, the exponent is taken over only the numerator. It should have been taken over both the numerator and denominator as shown below.

`2((3)/(5)) ^(3)=2((3^3)/(5^3))`

The correct workings therefore is:

`2((3)/(5)) ^(3)=2((3^3)/(5^3))=2((3X3X3)/(5X5X5))=2((27)/(125))=(54)/(125)`