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

To find the value of n that makes the equation true, we need to analyze the terms given: 2x9yn, 4x2y10, and 8x11y20. At first glance, each term seems to follow the pattern of a coefficient, a variable (x or y), and an exponent (n or a number).

Let’s break down each term:

• First term: 2x⁹yⁿ
• Second term: 4x²y¹⁰
• Third term: 8x¹¹y²⁰

To find a commonality or rule that connects these terms, we can inspect the coefficients (2, 4, and 8). These look like powers of 2:

• 2 = 2¹
• 4 = 2²
• 8 = 2³

This suggests that these coefficients follow a pattern of increasing by powers of 2. Now, let’s look at the exponents of x:

• First term: 9
• Second term: 2
• Third term: 11

There doesn’t seem to be an immediate pattern here, but we notice that we have a mix of values: 9, 2, and 11. The exponents of y also need to be considered:

• First term: n
• Second term: 10
• Third term: 20

For the exponents of y, we can see that they are increasing, notably from 10 to 20 shows a difference of 10. If we assume the first term’s exponent of y (which is n) fits this increasing sequence, we can infer a possible value for n.

If we set the pattern such that the difference between their values is consistent, a possible solution for n could be derived from averaging the previous two values (y¹⁰ and y²⁰), suggesting that n could very likely be 0. (Since 10 is directly 10 less than 20.) Thus, we can conclude:

The value of n that makes the equation appear true and follow the patterns is: n = 0.