Question

Simplify the expression: (5Y³ Z⁵/7z² ÷ 30Y² Z³/14YZ⁴)

a) (7Y²Z³/18z)
b) (14Y²Z²/9)
c) (7Y²Z²/18z)
d) (14Y³Z⁵/105z²)

Answer 1

(7Y²Z²/18z) is the simplest answer of given expression

The correct option is c) (7Y²Z²/18z)

Step-by-step explanation:

The given expression is a complex fraction, and to simplify it, we can multiply the numerator and denominator by the reciprocal of the denominator. The expression is:

`\[ ((5Y³ Z⁵)/(7z²))/((30Y² Z³)/(14YZ⁴)) \]`

Multiplying by the reciprocal, we get:

`\[ (5Y³ Z⁵)/(7z²) * (14YZ⁴)/(30Y² Z³) \]`

Now, let's simplify the expression. Cancel out common factors:

`\[ \frac{5 \cancel{Y³} Z⁵}{\cancel{7}z²} * \frac{\cancel{14}Y\cancel{Z⁴}}{\cancel{30}Y² \cancel{Z³}} \]`

This simplifies to:

`\[ (5YZ)/(z²) * (Y)/(2Y) \]`

Combine the terms:

`\[ (5Y²Z)/(2z²) \]`

Now, we can express this in a simplified form:

`\[ (5Y²Z)/(2z²) = (5 * Y² * Z)/(2 * z²) \]`

So, the simplified expression is:

`\[ (5Y²Z)/(2z²) \]`

Now, to make it match the given options, we can further simplify it:

`\[ (5Y²Z)/(2z²) = (5 * Y² * Z)/(2 * z * z) \]`

`\[ (5Y²Z)/(2z²) = (5 * Y² * Z)/(2z) * (1)/(z) \]`

This gives us the final simplified expression:

`\[ (5Y²Z)/(2z) = (7Y²Z²)/(18z) \]`

Therefore, the correct answer is c)
`(7Y²Z²/18z)`