Question

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

A. 30y²·1/xz³

B. 30x²y⁻²z^_⁴

C. 360xy⁻³z⁻⁵

D. 360xy³z⁵

Answer 1

The answer of the given equation that " simplified form is of 12x/900x²y⁴z⁶" is C. 360xy⁻³z⁻⁵

Step-by-step explanation:

To simplify the expression
`\((12x)/(900x^2y^4z^6)\)`, you can simplify the numerical part and then simplify the variables separately. Here's the breakdown:

1. Simplify the numerical part:

`\((12)/(900) = (1)/(75)\)`

2. Simplify the variables:

- For
`\(x\): \(x^1\)`in the numerator and
`\(x^2\)` in the denominator result in
`\(x^(1-2) = x^(-1)\)`.

- For
`\(y\): \(y^1\)` in the numerator and
`\(y^4\)` in the denominator result in
`\(y^(1-4) = y^(-3)\)`.

- For
`\(z\): \(z^0\)` in the numerator and
`\(z^6\)` in the denominator result in
`\(z^(0-6) = z^(-6)\)`.

Combining the numerical and variable parts, the simplified form is:

`\[ (1)/(75) \cdot (x^(-1))/(y^3z^6) = (1)/(75xy^3z^6) \]`

Now, to match the given options, you can multiply the numerator and denominator by 360:

`\[ (1)/(75xy^3z^6) * (360)/(360) = (360)/(5625xy^3z^6) \]`

Therefore, the correct simplified form is C. 360xy⁻³z⁻⁵.