Calculate the following, leaving your answer as a fraction (lowest) or in decimal form. Show work.
8(2+3)²
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2(5)²
I'll be glad to check your answer.
200/50=4
To calculate the expression (8(2+3)²)/(2(5)²), we can follow the order of operations (PEMDAS/BODMAS) to simplify it step by step.
Step 1: Evaluate the expression inside the parentheses.
Within the parentheses, we have (2+3), which equals 5. So, the expression becomes (8 * 5²)/(2 * 5²).
Step 2: Simplify the exponents.
The exponent 5² means 5 raised to the power of 2, which equals 5 * 5 = 25. Now, the expression becomes (8 * 25)/(2 * 25).
Step 3: Evaluate the multiplication.
Multiply the numbers outside the parentheses:
8 * 25 = 200
2 * 25 = 50
So, the expression becomes 200/50.
Step 4: Simplify the fraction.
To simplify the fraction, we can divide the numerator and denominator by their greatest common divisor (GCD), which is 50.
200 ÷ 50 = 4
50 ÷ 50 = 1
The expression simplifies to 4/1, which is equivalent to the whole number 4.
Alternatively, if we convert the fraction 4/1 into decimal form, it equals 4.