Math

QuestionCalculate the value of 106×2+8(47)23(4+8)\frac{10-6 \times 2+8}{(4-7)^{2}-3(4+8)}.

Studdy Solution

STEP 1

Assumptions1. We are given the expression 106×+8(47)3(4+8)\frac{10-6 \times+8}{(4-7)^{}-3(4+8)} . We need to simplify this expression following the order of operations (also known as BIDMAS/BODMAS/PEDMAS), which stands for Brackets, Indices (or Exponents), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).

STEP 2

First, we need to simplify the operations inside the brackets and perform the exponentiation.In the numerator, there are no brackets or exponents, so we perform the multiplication106×2+810-6 \times2+8In the denominator, we have brackets and an exponent, so we perform the operation inside the brackets first(47)2(4-7)^{2}

STEP 3

Now, perform the multiplication in the numerator and the subtraction in the denominator1012+810-12+8(3)2(-3)^{2}

STEP 4

Perform the subtraction in the numerator and the exponentiation in the denominator6699

STEP 5

Now, we need to perform the multiplication in the denominator3(4+8)3(4+8)

STEP 6

Perform the addition in the denominator3×123 \times12

STEP 7

Perform the multiplication in the denominator3636

STEP 8

Now, we have to perform the subtraction in the denominator36-36

STEP 9

Perform the subtraction in the denominator27-27

STEP 10

Now that we have simplified the numerator and the denominator, we can put them together to form the simplified expression627\frac{6}{-27}

STEP 11

This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is36/327/3\frac{6/3}{-27/3}

STEP 12

Perform the division in the numerator and the denominator29\frac{2}{-9}The simplified expression is 29\frac{2}{-9} or 29-\frac{2}{9}.

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