Final answer:
The value of n that makes the given equation true is 10, found by adding exponents of the like bases when multiplying algebraic expressions.
Step-by-step explanation:
To find the value of n that makes the equation true, we must multiply the given algebraic expressions. When multiplying expressions with exponents, you add the exponents of like bases. So, we have:
(2x⁹yⁿ)(4x²y¹⁰) = 8x^(9+2)y^(n+10)
This simplifies to 8x¹¹y^(n+10)
Comparing the result to 8x¹¹y²⁰, we can see that for the y exponents to match, n + 10 must equal 20. Solving for n gives us:
n + 10 = 20
n = 20 - 10
n = 10
Thus, the value of n that satisfies the equation is 10.