What will be the next row of numbers in the following pattern?
4, 16, 64
6, 36, 216
8, 64, 512

Options

A. 8, 68, 518
B. 10, 100, 1000
C. 10, 200, 2000
D. 10, 500, 5000

Answer

To find the next row of numbers in the given pattern, we can analyze the existing rows:

1. **First Row:** 4, 16, 64
- The first number is 4.
- The second number is \(4 \times 4 = 16\).
- The third number is \(4 \times 4 \times 4 = 64\).

2. **Second Row:** 6, 36, 216
- The first number is 6.
- The second number is \(6 \times 6 = 36\).
- The third number is \(6 \times 6 \times 6 = 216\).

3. **Third Row:** 8, 64, 512
- The first number is 8.
- The second number is \(8 \times 8 = 64\).
- The third number is \(8 \times 8 \times 8 = 512\).

Now, we can see a pattern:
- The first number in each row increases by 2: 4, 6, 8, ...
- The next number is the square of the first number.
- The last number is the cube of the first number.

Following this pattern:
- The next first number will be \(8 + 2 = 10\).
- The second number will be \(10 \times 10 = 100\).
- The third number will be \(10 \times 10 \times 10 = 1000\).

Thus, the next row of numbers in the pattern is **10, 100, 1000**.