How do you find the product of the following expression: 5x, 5, x², 10x, 25, x², 10x, 25, x², 25, x², 25?

To find the product of the expression 5x × 5 × x² × 10x × 25 × x² × 10x × 25 × x² × 25 × x² × 25, we can start by rearranging and grouping similar terms together.

First, let’s group the coefficients (the numerical values) and the variables separately:

• Coefficients: 5, 5, 10, 25, 25, 10, 25, 25
• Variables: x, x², x, x², x², x²

Calculating the product of the coefficients:

• 5 × 5 = 25
• 25 × 10 = 250
• 250 × 25 = 6250
• 6250 × 10 = 62500
• 62500 × 25 = 156250
• 156250 × 25 = 390625

Now, let’s calculate the powers of x:

• x (1 from the first term) + x (1 from the next x) + x² (2 from the first x²) + x² (2 from the second x²) + x² (2 from the third x²) = x^{1 + 1 + 2 + 2 + 2 = x8}

Combining the coefficients and the powered variable gives us:

390625 x8

So, the final product of the entire expression is 390625 x⁸.