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QuestionSimplify the expression: 6+∣9−2∣+825−2\frac{6+|9-2|+8^{2}}{5-2} and enter your answer as a number.

Studdy Solution

STEP 1

Assumptions1. The given expression is 6+∣9−∣+85−\frac{6+|9-|+8^{}}{5-} . We need to simplify this expression by following the order of operations, which is parentheses, exponents, multiplication and division (from left to right), addition and subtraction (from left to right). This is often remembered by the acronym PEMAS.

STEP 2

First, we need to simplify the absolute value in the numerator. Absolute value of a number is the non-negative value of a number without regard to its sign. So, ∣9−2∣|9-2| becomes ∣7∣|7|.
6+∣9−2∣+825−2=6+∣7∣+825−2\frac{6+|9-2|+8^{2}}{5-2} = \frac{6+|7|+8^{2}}{5-2}

STEP 3

The absolute value of7 is7 itself. So, replace ∣7∣|7| with7.
6+∣7∣+825−2=6+7+825−2\frac{6+|7|+8^{2}}{5-2} = \frac{6+7+8^{2}}{5-2}

STEP 4

Next, we need to calculate the exponent in the numerator. 828^{2} means8 multiplied by itself, which is64.
6+7+82−2=6+7+64−2\frac{6+7+8^{2}}{-2} = \frac{6+7+64}{-2}

STEP 5

Now, we can add the numbers in the numerator.
+7+645−2=775−2\frac{+7+64}{5-2} = \frac{77}{5-2}

STEP 6

Next, we need to subtract the numbers in the denominator.
775−2=773\frac{77}{5-2} = \frac{77}{3}

STEP 7

Finally, we can simplify the fraction by dividing the numerator by the denominator.
773=25.6666667\frac{77}{3} =25.6666667However, the problem asks for the answer in integer or fraction form. So, we leave the answer as 773\frac{77}{3}.

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