Solved on Dec 08, 2023

Evaluate the expression: $2ab^2c - 3(9+b) \div \frac{1}{4}a^2c^3 - abc$ where $a=2, b=5, c=3$ .

STEP 1

Assumptions
1. The values of the variables are given as $a=2$ , $b=5$ , and $c=3$ .
2. The expression to be evaluated is $2 a b^{2} c - 3(9+b) \div \frac{1}{4} a^{2} c^{3} - a b c$ .
3. The operations must be performed following the order of operations: parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).

STEP 2

First, we substitute the given values of $a$ , $b$ , and $c$ into the expression.
$2 \cdot 2 \cdot 5^{2} \cdot 3 - 3(9+5) \div \frac{1}{4} \cdot 2^{2} \cdot 3^{3} - 2 \cdot 5 \cdot 3$

STEP 3

Next, we calculate the value inside the parentheses $(9+5)$ .
$2 \cdot 2 \cdot 5^{2} \cdot 3 - 3(14) \div \frac{1}{4} \cdot 2^{2} \cdot 3^{3} - 2 \cdot 5 \cdot 3$

STEP 4

Now, we calculate the exponents $5^{2}$ , $2^{2}$ , and $3^{3}$ .
$2 \cdot 2 \cdot 25 \cdot 3 - 3(14) \div \frac{1}{4} \cdot 4 \cdot 27 - 2 \cdot 5 \cdot 3$

STEP 5

We perform the multiplication inside the first term $2 \cdot 2 \cdot 25 \cdot 3$ .
$4 \cdot 25 \cdot 3 - 3(14) \div \frac{1}{4} \cdot 4 \cdot 27 - 2 \cdot 5 \cdot 3$
$300 - 3(14) \div \frac{1}{4} \cdot 4 \cdot 27 - 2 \cdot 5 \cdot 3$

STEP 6

Multiply the second term $3(14)$ .
$300 - 42 \div \frac{1}{4} \cdot 4 \cdot 27 - 2 \cdot 5 \cdot 3$

STEP 7

We perform the division in the second term $42 \div \frac{1}{4}$ .
$300 - 42 \cdot 4 \cdot 27 - 2 \cdot 5 \cdot 3$

STEP 8

Now, we multiply $42 \cdot 4$ .
$300 - 168 \cdot 27 - 2 \cdot 5 \cdot 3$

STEP 9

Next, we multiply $168 \cdot 27$ .
$300 - 4536 - 2 \cdot 5 \cdot 3$

STEP 10

We perform the multiplication in the third term $2 \cdot 5 \cdot 3$ .
$300 - 4536 - 30$

STEP 11

Finally, we subtract the second and third terms from the first term.
$300 - 4536 - 30$

STEP 12

Subtract $4536$ from $300$ .
$-4236 - 30$

STEP 13

Subtract $30$ from $-4236$ .
$-4236 - 30 = -4266$
The evaluated expression is $-4266$ .

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Evaluate the expression: $2ab^2c - 3(9+b) \div \frac{1}{4}a^2c^3 - abc$ where $a=2, b=5, c=3$ .

STEP 1

STEP 2

First, we substitute the given values of $a$ , $b$ , and $c$ into the expression.
$2 \cdot 2 \cdot 5^{2} \cdot 3 - 3(9+5) \div \frac{1}{4} \cdot 2^{2} \cdot 3^{3} - 2 \cdot 5 \cdot 3$

STEP 3

Next, we calculate the value inside the parentheses $(9+5)$ .
$2 \cdot 2 \cdot 5^{2} \cdot 3 - 3(14) \div \frac{1}{4} \cdot 2^{2} \cdot 3^{3} - 2 \cdot 5 \cdot 3$

STEP 4

Now, we calculate the exponents $5^{2}$ , $2^{2}$ , and $3^{3}$ .
$2 \cdot 2 \cdot 25 \cdot 3 - 3(14) \div \frac{1}{4} \cdot 4 \cdot 27 - 2 \cdot 5 \cdot 3$

STEP 5

We perform the multiplication inside the first term $2 \cdot 2 \cdot 25 \cdot 3$ .
$4 \cdot 25 \cdot 3 - 3(14) \div \frac{1}{4} \cdot 4 \cdot 27 - 2 \cdot 5 \cdot 3$
$300 - 3(14) \div \frac{1}{4} \cdot 4 \cdot 27 - 2 \cdot 5 \cdot 3$

STEP 6

Multiply the second term $3(14)$ .
$300 - 42 \div \frac{1}{4} \cdot 4 \cdot 27 - 2 \cdot 5 \cdot 3$

STEP 7

We perform the division in the second term $42 \div \frac{1}{4}$ .
$300 - 42 \cdot 4 \cdot 27 - 2 \cdot 5 \cdot 3$

STEP 8

Now, we multiply $42 \cdot 4$ .
$300 - 168 \cdot 27 - 2 \cdot 5 \cdot 3$

STEP 9

Next, we multiply $168 \cdot 27$ .
$300 - 4536 - 2 \cdot 5 \cdot 3$

STEP 10

We perform the multiplication in the third term $2 \cdot 5 \cdot 3$ .
$300 - 4536 - 30$

STEP 11

Finally, we subtract the second and third terms from the first term.
$300 - 4536 - 30$

STEP 12

Subtract $4536$ from $300$ .
$-4236 - 30$

STEP 13

Subtract $30$ from $-4236$ .
$-4236 - 30 = -4266$
The evaluated expression is $-4266$ .

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Evaluate the expression: 2ab2c−3(9+b)÷14a2c3−abc2ab^2c - 3(9+b) \div \frac{1}{4}a^2c^3 - abc2ab2c−3(9+b)÷41​a2c3−abc where a=2,b=5,c=3a=2, b=5, c=3a=2,b=5,c=3.

STEP 1

STEP 2

First, we substitute the given values of aaa, bbb, and ccc into the expression.2⋅2⋅52⋅3−3(9+5)÷14⋅22⋅33−2⋅5⋅32 \cdot 2 \cdot 5^{2} \cdot 3 - 3(9+5) \div \frac{1}{4} \cdot 2^{2} \cdot 3^{3} - 2 \cdot 5 \cdot 32⋅2⋅52⋅3−3(9+5)÷41​⋅22⋅33−2⋅5⋅3

STEP 3

Next, we calculate the value inside the parentheses (9+5)(9+5)(9+5).2⋅2⋅52⋅3−3(14)÷14⋅22⋅33−2⋅5⋅32 \cdot 2 \cdot 5^{2} \cdot 3 - 3(14) \div \frac{1}{4} \cdot 2^{2} \cdot 3^{3} - 2 \cdot 5 \cdot 32⋅2⋅52⋅3−3(14)÷41​⋅22⋅33−2⋅5⋅3

STEP 4

Now, we calculate the exponents 525^{2}52, 222^{2}22, and 333^{3}33.2⋅2⋅25⋅3−3(14)÷14⋅4⋅27−2⋅5⋅32 \cdot 2 \cdot 25 \cdot 3 - 3(14) \div \frac{1}{4} \cdot 4 \cdot 27 - 2 \cdot 5 \cdot 32⋅2⋅25⋅3−3(14)÷41​⋅4⋅27−2⋅5⋅3

STEP 5

STEP 6

Multiply the second term 3(14)3(14)3(14).300−42÷14⋅4⋅27−2⋅5⋅3300 - 42 \div \frac{1}{4} \cdot 4 \cdot 27 - 2 \cdot 5 \cdot 3300−42÷41​⋅4⋅27−2⋅5⋅3

STEP 7

We perform the division in the second term 42÷1442 \div \frac{1}{4}42÷41​.300−42⋅4⋅27−2⋅5⋅3300 - 42 \cdot 4 \cdot 27 - 2 \cdot 5 \cdot 3300−42⋅4⋅27−2⋅5⋅3

STEP 8

Now, we multiply 42⋅442 \cdot 442⋅4.300−168⋅27−2⋅5⋅3300 - 168 \cdot 27 - 2 \cdot 5 \cdot 3300−168⋅27−2⋅5⋅3

STEP 9

Next, we multiply 168⋅27168 \cdot 27168⋅27.300−4536−2⋅5⋅3300 - 4536 - 2 \cdot 5 \cdot 3300−4536−2⋅5⋅3

STEP 10

We perform the multiplication in the third term 2⋅5⋅32 \cdot 5 \cdot 32⋅5⋅3.300−4536−30300 - 4536 - 30300−4536−30

STEP 11

Finally, we subtract the second and third terms from the first term.300−4536−30300 - 4536 - 30300−4536−30

STEP 12

Subtract 453645364536 from 300300300.−4236−30-4236 - 30−4236−30

STEP 13

Subtract 303030 from −4236-4236−4236.−4236−30=−4266-4236 - 30 = -4266−4236−30=−4266The evaluated expression is −4266-4266−4266.

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Evaluate the expression: $2ab^2c - 3(9+b) \div \frac{1}{4}a^2c^3 - abc$ where $a=2, b=5, c=3$ .

First, we substitute the given values of $a$ , $b$ , and $c$ into the expression.
$2 \cdot 2 \cdot 5^{2} \cdot 3 - 3(9+5) \div \frac{1}{4} \cdot 2^{2} \cdot 3^{3} - 2 \cdot 5 \cdot 3$

Next, we calculate the value inside the parentheses $(9+5)$ .
$2 \cdot 2 \cdot 5^{2} \cdot 3 - 3(14) \div \frac{1}{4} \cdot 2^{2} \cdot 3^{3} - 2 \cdot 5 \cdot 3$

Now, we calculate the exponents $5^{2}$ , $2^{2}$ , and $3^{3}$ .
$2 \cdot 2 \cdot 25 \cdot 3 - 3(14) \div \frac{1}{4} \cdot 4 \cdot 27 - 2 \cdot 5 \cdot 3$

Multiply the second term $3(14)$ .
$300 - 42 \div \frac{1}{4} \cdot 4 \cdot 27 - 2 \cdot 5 \cdot 3$

We perform the division in the second term $42 \div \frac{1}{4}$ .
$300 - 42 \cdot 4 \cdot 27 - 2 \cdot 5 \cdot 3$

Now, we multiply $42 \cdot 4$ .
$300 - 168 \cdot 27 - 2 \cdot 5 \cdot 3$

Next, we multiply $168 \cdot 27$ .
$300 - 4536 - 2 \cdot 5 \cdot 3$

We perform the multiplication in the third term $2 \cdot 5 \cdot 3$ .
$300 - 4536 - 30$

Finally, we subtract the second and third terms from the first term.
$300 - 4536 - 30$

Subtract $4536$ from $300$ .
$-4236 - 30$

Subtract $30$ from $-4236$ .
$-4236 - 30 = -4266$
The evaluated expression is $-4266$ .