calculate the following, leaving your answer as a fraction (lowest) or in decimal. Show your work

8(2+3²
---------
2(5)²

Is the numerator supposed to be

8(2+3)^2

?

yes it is supposed to be 8(2+3)^2

To calculate the expression 8(2+3²) / 2(5)², let's start by simplifying the numerator and denominator separately.

First, let's simplify the numerator: 8(2 + 3²).

Step 1: Calculate the exponent: 3² = 3 * 3 = 9.

Now, we have 8(2 + 9) for the numerator.

Step 2: Perform the sum inside the parentheses: 2 + 9 = 11.

Now, we have 8(11) for the numerator.

Step 3: Multiply: 8 * 11 = 88.

Now, let's simplify the denominator: 2(5)².

Step 1: Calculate the exponent: 5² = 5 * 5 = 25.

Now, we have 2(25) for the denominator.

Step 2: Multiply: 2 * 25 = 50.

Now, we have the fraction 88/50.

To reduce the fraction to its lowest terms, we can find the greatest common divisor (GCD) of both numerator and denominator, and divide both by the GCD.

Step 1: Find the GCD of 88 and 50.

The factors of 88 are: 1, 2, 4, 8, 11, 22, 44, 88.
The factors of 50 are: 1, 2, 5, 10, 25, 50.

The GCD of 88 and 50 is 2.

Step 2: Divide both numerator and denominator by the GCD (2).

88 / 2 = 44
50 / 2 = 25

Therefore, the simplified fraction is 44/25.

The decimal representation of 44/25 is approximately 1.76.