Question

What is the simplified form of 12x/900x²y4z6?

O 30y²|xz³|
O 30x²y2z4
O 360xy²|xz³|
O 360xy²|z³|

Answer 1

`360xy^2|xz^3|`

Explanation:

Given expression:

`12x √(900x^2y^4z^6)`

`\textsf{Apply radical rule} \quad √(ab)=√(a)√(b):`

`\implies 12x √(900)√(x^2)√(y^4)√(z^6)`

Replace 900 with 30² :

`\implies 12x √(30^2)√(x^2)√(y^4)√(z^6)`

`\textsf{Apply radical rule} \quad √(a^2)=a, \quad a \geq 0:`

`\implies 12x \cdot 30|x|√(y^4)√(z^6)`

`\implies 360x|x|√(y^4)√(z^6)`

(We need to use the absolute value of √x² since the x term was originally to the power of 2, which means the value of x² is always positive since the exponent is even).

`\textsf{Apply exponent rule} \quad √(a^m)=a^{(m)/(2)}:`

`\implies 360x|x|\cdot y^{(4)/(2)}\cdot z^{(6)/(2)}`

Simplify:

`\implies 360xy^2|xz^3|`

(We need to use the absolute value of z³ since the z term was original to the power of 6, which means the value of z⁶ is always positive since the exponent is even).