QuestionCalculate $\frac{7+3^{2}}{4^{2} \cdot 2}$ .

Studdy Solution

STEP 1

Assumptions1. Follow 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 solve the exponentiation in the numerator and the denominator.
In the numerator, we have $^{2}$ and in the denominator, we have $4^{2}$ .

STEP 3

Calculate the values of $3^{2}$ and $^{2}$ .
$3^{2} =9$ $^{2} =16$

STEP 4

Replace $3^{2}$ with9 and $4^{2}$ with16 in the original expression.
$\frac{7+3^{2}}{4^{2} \cdot2} = \frac{7+9}{16 \cdot2}$

STEP 5

Next, perform the addition in the numerator.
$\frac{7+9}{16 \cdot2} = \frac{16}{16 \cdot2}$

STEP 6

Then, perform the multiplication in the denominator.
$\frac{16}{16 \cdot2} = \frac{16}{32}$

STEP 7

Finally, perform the division.
$\frac{16}{32} =0.5$ So, $\frac{7+3^{2}}{4^{2} \cdot2} =0.5$ .

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QuestionCalculate $\frac{7+3^{2}}{4^{2} \cdot 2}$ .

Studdy Solution

STEP 1

Assumptions1. Follow 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 solve the exponentiation in the numerator and the denominator.
In the numerator, we have $^{2}$ and in the denominator, we have $4^{2}$ .

STEP 3

Calculate the values of $3^{2}$ and $^{2}$ .
$3^{2} =9$ $^{2} =16$

STEP 4

Replace $3^{2}$ with9 and $4^{2}$ with16 in the original expression.
$\frac{7+3^{2}}{4^{2} \cdot2} = \frac{7+9}{16 \cdot2}$

STEP 5

Next, perform the addition in the numerator.
$\frac{7+9}{16 \cdot2} = \frac{16}{16 \cdot2}$

STEP 6

Then, perform the multiplication in the denominator.
$\frac{16}{16 \cdot2} = \frac{16}{32}$

STEP 7

Finally, perform the division.
$\frac{16}{32} =0.5$ So, $\frac{7+3^{2}}{4^{2} \cdot2} =0.5$ .

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QuestionCalculate 7+3242⋅2\frac{7+3^{2}}{4^{2} \cdot 2}42⋅27+32​.

Studdy Solution

STEP 1

Assumptions1. Follow 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 solve the exponentiation in the numerator and the denominator.In the numerator, we have 2^{2}2 and in the denominator, we have 424^{2}42.

STEP 3

Calculate the values of 323^{2}32 and 2^{2}2.32=93^{2} =932=92=16^{2} =162=16

STEP 4

Replace 323^{2}32 with9 and 424^{2}42 with16 in the original expression.7+3242⋅2=7+916⋅2\frac{7+3^{2}}{4^{2} \cdot2} = \frac{7+9}{16 \cdot2}42⋅27+32​=16⋅27+9​

STEP 5

Next, perform the addition in the numerator.7+916⋅2=1616⋅2\frac{7+9}{16 \cdot2} = \frac{16}{16 \cdot2}16⋅27+9​=16⋅216​

STEP 6

Then, perform the multiplication in the denominator.1616⋅2=1632\frac{16}{16 \cdot2} = \frac{16}{32}16⋅216​=3216​

STEP 7

Finally, perform the division.1632=0.5\frac{16}{32} =0.53216​=0.5So, 7+3242⋅2=0.5\frac{7+3^{2}}{4^{2} \cdot2} =0.542⋅27+32​=0.5.

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QuestionCalculate $\frac{7+3^{2}}{4^{2} \cdot 2}$ .

First, we need to solve the exponentiation in the numerator and the denominator.
In the numerator, we have $^{2}$ and in the denominator, we have $4^{2}$ .

Calculate the values of $3^{2}$ and $^{2}$ .
$3^{2} =9$ $^{2} =16$

Replace $3^{2}$ with9 and $4^{2}$ with16 in the original expression.
$\frac{7+3^{2}}{4^{2} \cdot2} = \frac{7+9}{16 \cdot2}$

Next, perform the addition in the numerator.
$\frac{7+9}{16 \cdot2} = \frac{16}{16 \cdot2}$

Then, perform the multiplication in the denominator.
$\frac{16}{16 \cdot2} = \frac{16}{32}$

Finally, perform the division.
$\frac{16}{32} =0.5$ So, $\frac{7+3^{2}}{4^{2} \cdot2} =0.5$ .