What value of n makes the equation true? (2x⁹yⁿ)(4x²y¹⁰) = 8x¹¹y²⁰?
(a) 1  (b) 2  (c) 10  (d) 30

Solution:

An exponent of a number shows how many times we are multiplying a number by itself.

Let's use the concept of multiplying exponents to find the value of n.

(2x⁹yⁿ)(4x²y¹⁰) = 8x¹¹y²⁰

Multiplying exponents with same base: a^m × aⁿ = a^{{m + n}}

Apply the Rule of Multiplying Exponents on the powers of x.

⇒ x⁹ × x²  = x^{9 + 2} = x¹¹

The powers of y work the same way.

⇒ yⁿ × y¹⁰ = y^{n + 10} = y²⁰

Since y^{10 + 10} = y²⁰  So, n = 10.

Therefore, the value of n is 10.

What value of n makes the equation true? (2x⁹yⁿ)(4x²y¹⁰) = 8x¹¹y²⁰?

Summary:

The value of n in the equation (2x⁹yⁿ)(4x²y¹⁰) = 8x¹¹y²⁰ is 10.