Question

What value of n makes the equation true?


`(2x^9y^n)(4x^2y^10)=8x^1^1y^2^0`
A. 1
B. 2
C. 10
D. 30

Answer 1

C. 10

Explanation:

got it right on the quiz

Answer 2

C. 10

Explanation

(2x⁹yⁿ)(4x²y¹⁰)=8x¹¹y²⁰

(2x⁹yⁿ)(4x²y¹⁰) = (2×4)(x⁹⁺²yⁿ⁺¹⁰)

= 8 × x¹¹ × y⁽ⁿ⁺¹⁰⁾

= 8x¹¹y⁽ⁿ⁺¹⁰⁾

∴ 8x¹¹y⁽ⁿ⁺¹⁰⁾ = 8x¹¹y²⁰

If the left hand side is equal to the right hand side, then;

y⁽ⁿ⁺¹⁰⁾ = y²⁰

n + 10 = 20

n = 20 - 10

= 10