Question Simplify the numerical expression $8^{2}+7(-2-5)+3$ using the rules for order of operations.

Studdy Solution

STEP 1

Assumptions
1. We need to follow the order of operations, also known as PEMDAS/BODMAS (Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
2. The given expression is $8^{2}+7(-2-5)+3$ .

STEP 2

First, we need to simplify the expression inside the parentheses.
$-2 - 5$

STEP 3

Perform the subtraction inside the parentheses.
$-2 - 5 = -7$

STEP 4

Replace the original parentheses in the expression with the result from STEP_3.
$8^{2} + 7(-7) + 3$

STEP 5

Next, we need to apply the exponentiation part of the order of operations.
$8^{2}$

STEP 6

Calculate the exponentiation.
$8^{2} = 64$

STEP 7

Replace the exponentiation in the expression with the result from STEP_6.
$64 + 7(-7) + 3$

STEP 8

Now, we need to perform the multiplication.
$7 \times (-7)$

STEP 9

Calculate the multiplication.
$7 \times (-7) = -49$

STEP 10

Replace the multiplication in the expression with the result from STEP_9.
$64 - 49 + 3$

STEP 11

Now, we perform the addition and subtraction from left to right.
First, add 64 and -49.
$64 - 49$

STEP 12

Calculate the addition.
$64 - 49 = 15$

STEP 13

Replace the addition in the expression with the result from STEP_12.
$15 + 3$

STEP 14

Finally, perform the last addition.
$15 + 3$

STEP 15

Calculate the final addition.
$15 + 3 = 18$
The simplified expression is 18.

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Question Simplify the numerical expression $8^{2}+7(-2-5)+3$ using the rules for order of operations.

Studdy Solution

STEP 1

Assumptions
1. We need to follow the order of operations, also known as PEMDAS/BODMAS (Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
2. The given expression is $8^{2}+7(-2-5)+3$ .

STEP 2

First, we need to simplify the expression inside the parentheses.
$-2 - 5$

STEP 3

Perform the subtraction inside the parentheses.
$-2 - 5 = -7$

STEP 4

Replace the original parentheses in the expression with the result from STEP_3.
$8^{2} + 7(-7) + 3$

STEP 5

Next, we need to apply the exponentiation part of the order of operations.
$8^{2}$

STEP 6

Calculate the exponentiation.
$8^{2} = 64$

STEP 7

Replace the exponentiation in the expression with the result from STEP_6.
$64 + 7(-7) + 3$

STEP 8

Now, we need to perform the multiplication.
$7 \times (-7)$

STEP 9

Calculate the multiplication.
$7 \times (-7) = -49$

STEP 10

Replace the multiplication in the expression with the result from STEP_9.
$64 - 49 + 3$

STEP 11

Now, we perform the addition and subtraction from left to right.
First, add 64 and -49.
$64 - 49$

STEP 12

Calculate the addition.
$64 - 49 = 15$

STEP 13

Replace the addition in the expression with the result from STEP_12.
$15 + 3$

STEP 14

Finally, perform the last addition.
$15 + 3$

STEP 15

Calculate the final addition.
$15 + 3 = 18$
The simplified expression is 18.

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Question Simplify the numerical expression 82+7(−2−5)+38^{2}+7(-2-5)+382+7(−2−5)+3 using the rules for order of operations.

Studdy Solution

STEP 1

Assumptions1. We need to follow the order of operations, also known as PEMDAS/BODMAS (Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).2. The given expression is 82+7(−2−5)+38^{2}+7(-2-5)+382+7(−2−5)+3.

STEP 2

First, we need to simplify the expression inside the parentheses.−2−5-2 - 5−2−5

STEP 3

Perform the subtraction inside the parentheses.−2−5=−7-2 - 5 = -7−2−5=−7

STEP 4

Replace the original parentheses in the expression with the result from STEP_3.82+7(−7)+38^{2} + 7(-7) + 382+7(−7)+3

STEP 5

Next, we need to apply the exponentiation part of the order of operations.828^{2}82

STEP 6

Calculate the exponentiation.82=648^{2} = 6482=64

STEP 7

Replace the exponentiation in the expression with the result from STEP_6.64+7(−7)+364 + 7(-7) + 364+7(−7)+3

STEP 8

Now, we need to perform the multiplication.7×(−7)7 \times (-7)7×(−7)

STEP 9

Calculate the multiplication.7×(−7)=−497 \times (-7) = -497×(−7)=−49

STEP 10

Replace the multiplication in the expression with the result from STEP_9.64−49+364 - 49 + 364−49+3

STEP 11

Now, we perform the addition and subtraction from left to right.First, add 64 and -49.64−4964 - 4964−49

STEP 12

Calculate the addition.64−49=1564 - 49 = 1564−49=15

STEP 13

Replace the addition in the expression with the result from STEP_12.15+315 + 315+3

STEP 14

Finally, perform the last addition.15+315 + 315+3

STEP 15

Calculate the final addition.15+3=1815 + 3 = 1815+3=18The simplified expression is 18.

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Question Simplify the numerical expression $8^{2}+7(-2-5)+3$ using the rules for order of operations.

Assumptions
1. We need to follow the order of operations, also known as PEMDAS/BODMAS (Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
2. The given expression is $8^{2}+7(-2-5)+3$ .

First, we need to simplify the expression inside the parentheses.
$-2 - 5$

Perform the subtraction inside the parentheses.
$-2 - 5 = -7$

Replace the original parentheses in the expression with the result from STEP_3.
$8^{2} + 7(-7) + 3$

Next, we need to apply the exponentiation part of the order of operations.
$8^{2}$

Calculate the exponentiation.
$8^{2} = 64$

Replace the exponentiation in the expression with the result from STEP_6.
$64 + 7(-7) + 3$

Now, we need to perform the multiplication.
$7 \times (-7)$

Calculate the multiplication.
$7 \times (-7) = -49$

Replace the multiplication in the expression with the result from STEP_9.
$64 - 49 + 3$

Now, we perform the addition and subtraction from left to right.
First, add 64 and -49.
$64 - 49$

Calculate the addition.
$64 - 49 = 15$

Replace the addition in the expression with the result from STEP_12.
$15 + 3$

Finally, perform the last addition.
$15 + 3$

Calculate the final addition.
$15 + 3 = 18$
The simplified expression is 18.