Which expression is equivalent to 9x^5 y^16 / 45x^5y^4? a) y^12 / 5 b) y^12 / 36 c) xy^4 / 5 d) xy^4 / 36

Option A is correct, i. e. y¹² / 5

Step-by-step explanation:

Given the expression is (9x^5 y^16) / (45x^5y^4)

(9 x⁵ y¹⁶) / (45 x⁵ y⁴) = (9/45) * (x⁵ x⁻⁵) * (y¹⁶ y⁻⁴)

(9 x⁵ y¹⁶) / (45 x⁵ y⁴) = (1/5) * (x⁵⁻⁵) * (y¹⁶⁻⁴)

(9 x⁵ y¹⁶) / (45 x⁵ y⁴) = (1/5) * (x⁰) * (y¹²)

(9 x⁵ y¹⁶) / (45 x⁵ y⁴) = (1/5) * (1) * (y¹²)

(9 x⁵ y¹⁶) / (45 x⁵ y⁴) = y¹² / 5

Hence, option A is correct, i. e. y¹² / 5

Choice a is correct answer.

Step-by-step explanation:

Given expression is:

9x⁵y¹⁶ / 45x⁵y⁴

We have to find equivalent expression by simplifying above expression.

We use following formulas to solve it.

x⁻ᵃ = 1/xᵃ (formula 1)

xᵃ * xᵇ = xᵃ⁺ᵇ (formula 2)

As we know that

45 = 9*5

9x⁵y¹⁶ / 9*5 x⁵y⁴

x⁵y¹⁶ / 5 x⁵y⁴

Using formula 1 in above expression, we have

1 / 5*x⁵*y¹⁶*x⁻⁵y⁻⁴

Using formula 2 in above expression, we have

1 / 5*x⁵⁻⁵ * y¹⁶⁻⁴

1/5 * x⁰*y¹²

As x⁰ = 1

1/5 * 1 * y¹²

y¹² / 5 which is the answer.