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What is #(5^3 + 25 -: -1) -: -4#, using order of operations?

Answer 1

#25#

Always count the number of terms first. That will tell you where to start. Each term must simplify to a single answer. The answers are added or subtracted in the last step.

#(5^3 + 25 -: -1) -: -4 " there is only 1 term"#

However within the brackets there are several terms, each needs to calculated separately.

#(color(red)(5^3)color(blue)( + 25 -: -1)) -: -4#

#(color(red)(125)color(blue)( -25)) -: -4#

#color(magenta)((100) -: -4)#

#25#

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Answer 2

Avery Alexander

Using the order of operations (PEMDAS/BODMAS), the expression (5^3 + 25 ÷ -1) ÷ -4 evaluates as follows:

Exponents: (5^3 = 5 \times 5 \times 5 = 125)
Division: (25 ÷ -1 = -25)
Addition: (125 + (-25) = 100)
Division: (100 ÷ -4 = -25)

Therefore, ((5^3 + 25 ÷ -1) ÷ -4) equals (-25).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.