Solved on Jan 18, 2024

Evaluate the expression $\frac{1}{6}\left(\sqrt{36} \div \frac{1}{3^{2}}\right)+4^{2} \div 8$ and provide the value.

STEP 1

Assumptions
1. We need to evaluate the expression: $\frac{1}{6}\left(\sqrt{36} \div \frac{1}{3^{2}}\right)+4^{2} \div 8$
2. We will follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right), commonly abbreviated as PEMDAS.

STEP 2

First, we will simplify the expression inside the parentheses, starting with the square root.
$\sqrt{36} = 6$

STEP 3

Next, we will evaluate the exponent inside the parentheses.
$3^{2} = 9$

STEP 4

Now we will perform the division inside the parentheses.
$\sqrt{36} \div \frac{1}{3^{2}} = 6 \div \frac{1}{9}$

STEP 5

Dividing by a fraction is the same as multiplying by its reciprocal.
$6 \div \frac{1}{9} = 6 \times 9$

STEP 6

Calculate the multiplication result.
$6 \times 9 = 54$

STEP 7

Now we will multiply the result by the fraction outside the parentheses.
$\frac{1}{6} \times 54$

STEP 8

Calculate the multiplication of the fraction with the number.
$\frac{1}{6} \times 54 = \frac{54}{6}$

STEP 9

Simplify the fraction.
$\frac{54}{6} = 9$

STEP 10

Next, we will evaluate the exponent in the second term of the expression.
$4^{2} = 16$

STEP 11

Now we will perform the division in the second term.
$16 \div 8$

STEP 12

Calculate the division result.
$16 \div 8 = 2$

STEP 13

Finally, we will add the results of the two terms.
$9 + 2$

STEP 14

Calculate the sum.
$9 + 2 = 11$
The value of the expression is 11.

Was this helpful?

Evaluate the expression $\frac{1}{6}\left(\sqrt{36} \div \frac{1}{3^{2}}\right)+4^{2} \div 8$ and provide the value.

STEP 1

STEP 2

First, we will simplify the expression inside the parentheses, starting with the square root.
$\sqrt{36} = 6$

STEP 3

Next, we will evaluate the exponent inside the parentheses.
$3^{2} = 9$

STEP 4

Now we will perform the division inside the parentheses.
$\sqrt{36} \div \frac{1}{3^{2}} = 6 \div \frac{1}{9}$

STEP 5

Dividing by a fraction is the same as multiplying by its reciprocal.
$6 \div \frac{1}{9} = 6 \times 9$

STEP 6

Calculate the multiplication result.
$6 \times 9 = 54$

STEP 7

Now we will multiply the result by the fraction outside the parentheses.
$\frac{1}{6} \times 54$

STEP 8

Calculate the multiplication of the fraction with the number.
$\frac{1}{6} \times 54 = \frac{54}{6}$

STEP 9

Simplify the fraction.
$\frac{54}{6} = 9$

STEP 10

Next, we will evaluate the exponent in the second term of the expression.
$4^{2} = 16$

STEP 11

Now we will perform the division in the second term.
$16 \div 8$

STEP 12

Calculate the division result.
$16 \div 8 = 2$

STEP 13

Finally, we will add the results of the two terms.
$9 + 2$

STEP 14

Calculate the sum.
$9 + 2 = 11$
The value of the expression is 11.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Evaluate the expression 16(36÷132)+42÷8\frac{1}{6}\left(\sqrt{36} \div \frac{1}{3^{2}}\right)+4^{2} \div 861​(36​÷321​)+42÷8 and provide the value.

STEP 1

STEP 2

First, we will simplify the expression inside the parentheses, starting with the square root.36=6\sqrt{36} = 636​=6

STEP 3

Next, we will evaluate the exponent inside the parentheses.32=93^{2} = 932=9

STEP 4

Now we will perform the division inside the parentheses.36÷132=6÷19\sqrt{36} \div \frac{1}{3^{2}} = 6 \div \frac{1}{9}36​÷321​=6÷91​

STEP 5

Dividing by a fraction is the same as multiplying by its reciprocal.6÷19=6×96 \div \frac{1}{9} = 6 \times 96÷91​=6×9

STEP 6

Calculate the multiplication result.6×9=546 \times 9 = 546×9=54

STEP 7

Now we will multiply the result by the fraction outside the parentheses.16×54\frac{1}{6} \times 5461​×54

STEP 8

Calculate the multiplication of the fraction with the number.16×54=546\frac{1}{6} \times 54 = \frac{54}{6}61​×54=654​

STEP 9

Simplify the fraction.546=9\frac{54}{6} = 9654​=9

STEP 10

Next, we will evaluate the exponent in the second term of the expression.42=164^{2} = 1642=16

STEP 11

Now we will perform the division in the second term.16÷816 \div 816÷8

STEP 12

Calculate the division result.16÷8=216 \div 8 = 216÷8=2

STEP 13

Finally, we will add the results of the two terms.9+29 + 29+2

STEP 14

Calculate the sum.9+2=119 + 2 = 119+2=11The value of the expression is 11.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Evaluate the expression $\frac{1}{6}\left(\sqrt{36} \div \frac{1}{3^{2}}\right)+4^{2} \div 8$ and provide the value.

First, we will simplify the expression inside the parentheses, starting with the square root.
$\sqrt{36} = 6$

Next, we will evaluate the exponent inside the parentheses.
$3^{2} = 9$

Now we will perform the division inside the parentheses.
$\sqrt{36} \div \frac{1}{3^{2}} = 6 \div \frac{1}{9}$

Dividing by a fraction is the same as multiplying by its reciprocal.
$6 \div \frac{1}{9} = 6 \times 9$

Calculate the multiplication result.
$6 \times 9 = 54$

Now we will multiply the result by the fraction outside the parentheses.
$\frac{1}{6} \times 54$

Calculate the multiplication of the fraction with the number.
$\frac{1}{6} \times 54 = \frac{54}{6}$

Simplify the fraction.
$\frac{54}{6} = 9$

Next, we will evaluate the exponent in the second term of the expression.
$4^{2} = 16$

Now we will perform the division in the second term.
$16 \div 8$

Calculate the division result.
$16 \div 8 = 2$

Finally, we will add the results of the two terms.
$9 + 2$

Calculate the sum.
$9 + 2 = 11$
The value of the expression is 11.