Question

Javier simplified the expression below. Find and describe the three mistakes he made.

Answer 1

`( (20x)/(5x^8))^-^3`

Take out the constants


`( (20)/(5) * (x)/(x^8) ) ^-^3`


`(4*(x)/(x^8) ) ^-^3`

Use the rule :
`\frac{{x}^(a)}{{x}^(b)}={x}^(a-b)`


`(4x^1^-^8)^-^3`


`(4x^-^7)^-^3`

Use the negative power rule :
`{x}^(-a)=\frac{1}{{x}^(a)}`


`(1)/(4(x^-^7))^-^3`


`(1)/(4^3(x^-^7))^-^3`


`(1)/(64x^-^2^1)`


`(1)/(64* (1)/(x^2^1))`


`\frac{1}{64 \frac{}{x^2^1}}`


`= (x^2^1)/(64)`

Answer 2

On Ed2018

1) Javier did not raise the coefficients to the third power

2) when Javier raised x to the third power, he wrote that (x^1)^3=x^4, but it equals x^3

3) In the last step, Javier divided the exponents. He should have used the quotient of powers property and subtracted them.