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

1 Answer
Alan P.
Dec 30, 2016

#(10+2(-5))/((2^2)(3))=color(green)(5)#

Explanation:

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#

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