(5a³b)²/10a²b

How would I begin solving this? Thank you!

1a^4*b/2

25/10 = 2.5

a^6/a^2 = a^4
b^2/b = b
so
2.5 a^4 b or (25/10) a^4 b

To simplify the expression (5a³b)²/10a²b, we can follow the order of operations which is also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).

1. Begin by simplifying the expression inside the parentheses, (5a³b)².
- To square a binomial, you multiply it by itself. In this case, we have (5a³b)², so we multiply (5a³b) by itself.
- (5a³b)² = (5a³b) * (5a³b)
- To multiply two binomials, we multiply each term in the first binomial by each term in the second binomial.
- (5a³b) * (5a³b) = 5 * 5 * a³ * a³ * b * b
- Simplifying further, we get: 25a^6b^2

2. Now let's simplify the rest of the expression: 25a^6b^2 / 10a²b.
- When dividing with the same base, we subtract the exponents.
- In this case, we have a^6 / a^2, which gives us a^(6-2) = a^4.
- Similarly, b^2 / b gives us b^(2-1) = b.
- So our expression becomes: 25a^4b / 10ab.

3. Finally, divide the coefficients.
- The coefficient of 25a^4b is 25.
- The coefficient of 10ab is 10.
- Dividing 25 by 10 gives us 2.5.
- Therefore, our final simplified expression is: 2.5a^4b.

So, the simplified form of (5a³b)²/10a²b is 2.5a^4b.