Question

Find the correct missing value: y⁹ (x^²y = ³ ) ⁰ 12 X =​

Answer 1

-3

Explanation:

Given equation:

`\implies (x^4y^(-3))^n=(y^9)/(x^(12))`

`\textsf{Apply exponent rule} \quad (1)/(a^n)=a^(-n):`

`\implies (x^4y^(-3))^n=x^(-12)y^9`

Rewrite -12 as (4 × -3) and 9 as (-3 × -3):

`\implies (x^4y^(-3))^n=x^((4 * -3))y^((-3 * -3))`

`\textsf{Apply exponent rule} \quad a^(bc)=(a^b)^c`:

`\implies (x^4y^(-3))^n=(x^4)^(-3)(y^(-3))^(-3)`

`\textsf{Apply exponent rule} \quad a^c b^c=(ab)^c`

`\implies (x^4y^(-3))^n=(x^4y^(-3))^(-3)`

Therefore, the missing value is -3