Question

Anja simplified the expression 10x-5/-5x^10 to 15/x^15. What mistake did Anja make?

a. She divided the exponent instead of subtracting them
b. She divided the coefficients instead of subtracting them
c. She subtracted the coefficients instead of dividing them
d. She subtracted the exponents instead of dividing them

Answer 1

C.

The coefficients 10 and -5 were supposed to be divided to give -2 as the coefficient.

Answer 2

Answer: option c. She subtracted the coefficients instead of dividing them

Explanation:

1) Starting expression (given):

$\frac{10x^{-5}}{-5x^{10}}$

2) Simplified expression (given)

$\frac{15}{x^{15}}$

3) Note that if you do the operations correctly you get:

i) By dividing the coefficients:

$-\frac{2x^{-5}}{x^{10}}$

ii) By subtracting the exponents

$-\frac{2}{x^{15}}$

And that is the correct result.

4) But if you subtract the coefficients, instead of dividing them, then you get 10 - ( - 5) = 10 + 5 = 15

Which is what she obtained in the numerator. And this is wrong, because the coefficients must be divided.

It is the exponents what you subtract, as per the rule of quotient of powers.