Question

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

Answer 1

Choice a is correct answer.

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.

Answer 2

Option A is correct, i.e. y¹² /5

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