How do you evaluate #\frac { 10+ 2( - 5) ^ { 2} } { ( 2^ { 2} ) ( 3) }#?

Question

Zoe Adams · Accepted Answer

#(10+2(-5))/((2^2)(3))=color(green)(5)# Using P E DM AS Evaluate: #color(white)("XXX")#Parentheses first #color(white)("XXXXXX")#for the given example #color(white)("XXXXXX")#parentheses are only used to clarify multiplication. #color(white)("XXX")#Exponentiation next #color(white)("XXX")#Division and Multiplication next (left to right) #color(white)("XXX")#Addition and Subtraction last (left to right) Because of the "left-to-right" requirement we will first convert the given expression into a linear form: #color(white)("XXX")(10+2(-5)^2)/((2^2)(3))# #color(white)("XXXXXX")=(10+2(-5)^2) div ((2^2)(3))# #color(white)("XXXXXX")=(10+2 * 25) div((2^2)(3))# #color(white)("XXXXXX")=(10+50) div ((2^2) (3))# #color(white)("XXXXXX")=60 div ((2^2)(3))# #color(white)("XXXXXX")=60 div (4 * 3)# #color(white)("XXXXXX")=60 div 12# #color(white)("XXXXXX")=5#

Emery Allen · Answer

undefined To evaluate $ \frac{10 + 2(-5)^2}{(2^2)(3)} $, follow the order of operations (PEMDAS/BODMAS):

1. First, calculate the expression within the parentheses and exponent: $ (-5)^2 = 25 $.
2. Then, substitute this value into the expression: $ \frac{10 + 2(25)}{(2^2)(3)} $.
3. Next, evaluate the exponent $ 2^2 = 4 $.
4. Substitute this value into the expression: $ \frac{10 + 2(25)}{4(3)} $.
5. Now, perform the multiplication: $ 2(25) = 50 $ and $ 4(3) = 12 $.
6. Then, add the remaining terms: $ 10 + 50 = 60 $.
7. Finally, perform the division: $ \frac{60}{12} = 5 $.

Therefore, $ \frac{10 + 2(-5)^2}{(2^2)(3)} = 5 $.