Question

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

Answer 1

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.

Answer 2

$( \dfrac{20x}{5x^8})^-^3$ 

Take out the constants

$( \dfrac{20}{5} * \dfrac{x}{x^8} ) ^-^3$ 

$(4*\dfrac{x}{x^8} ) ^-^3$ 

Use the rule : $\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}$ 

$(4x^1^-^8)^-^3$ 

$(4x^-^7)^-^3$ 

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

$\frac{1}{4(x^-^7)}^-^3$ 

$\frac{1}{4^3(x^-^7)}^-^3$ 

$\dfrac{1}{64x^-^2^1}$ 

$\dfrac{1}{64* \dfrac{1}{x^2^1}}$ 

$\dfrac{1}{64 \dfrac{}{x^2^1}}$ 

$= \dfrac{x^2^1}{64}$