Solved on Dec 15, 2023

Evaluate the expression $2 \cdot(-1 \div 6)^{4}$ to find the equivalent value.

STEP 1

Assumptions
1. The expression to evaluate is $2 \cdot(-1 \div 6)^{4}$ .
2. The operations must be performed following the order of operations: parentheses, exponents, multiplication and division from left to right.

STEP 2

First, we need to evaluate the expression inside the parentheses.
$(-1 \div 6)$

STEP 3

Perform the division inside the parentheses.
$(-1 \div 6) = -\frac{1}{6}$

STEP 4

Next, we need to raise the result of the division to the power of 4 as indicated by the exponent.
$\left(-\frac{1}{6}\right)^{4}$

STEP 5

When raising a negative fraction to an even power, the result is positive. We will raise both the numerator and the denominator to the power of 4.
$\left(-\frac{1}{6}\right)^{4} = \left(-1\right)^{4} \cdot \left(\frac{1}{6}\right)^{4}$

STEP 6

Calculate the value of the negative one raised to the fourth power.
$\left(-1\right)^{4} = 1$

STEP 7

Calculate the value of one-sixth raised to the fourth power.
$\left(\frac{1}{6}\right)^{4} = \frac{1^4}{6^4}$

STEP 8

Simplify the fraction.
$\frac{1^4}{6^4} = \frac{1}{1296}$

STEP 9

Combine the results from steps 6 and 8.
$\left(-\frac{1}{6}\right)^{4} = 1 \cdot \frac{1}{1296} = \frac{1}{1296}$

STEP 10

Now, we need to multiply the result by 2 as indicated by the expression.
$2 \cdot \frac{1}{1296}$

STEP 11

Perform the multiplication.
$2 \cdot \frac{1}{1296} = \frac{2}{1296}$

STEP 12

Simplify the fraction by dividing both the numerator and the denominator by the greatest common divisor, which is 2.
$\frac{2}{1296} = \frac{1}{648}$

STEP 13

Convert the fraction to a decimal to match the answer choices.
$\frac{1}{648} \approx 0.00154320987654321$

STEP 14

Round the decimal to three significant figures to match the answer choices.
$0.00154320987654321 \approx 0.00154$

STEP 15

Now we compare the result with the answer choices. The closest value to our result is 0.002.
The value equivalent to the expression $2 \cdot(-1 \div 6)^{4}$ is 0.002, which corresponds to answer choice c.

Was this helpful?

Evaluate the expression $2 \cdot(-1 \div 6)^{4}$ to find the equivalent value.

STEP 1

Assumptions
1. The expression to evaluate is $2 \cdot(-1 \div 6)^{4}$ .
2. The operations must be performed following the order of operations: parentheses, exponents, multiplication and division from left to right.

STEP 2

First, we need to evaluate the expression inside the parentheses.
$(-1 \div 6)$

STEP 3

Perform the division inside the parentheses.
$(-1 \div 6) = -\frac{1}{6}$

STEP 4

Next, we need to raise the result of the division to the power of 4 as indicated by the exponent.
$\left(-\frac{1}{6}\right)^{4}$

STEP 5

When raising a negative fraction to an even power, the result is positive. We will raise both the numerator and the denominator to the power of 4.
$\left(-\frac{1}{6}\right)^{4} = \left(-1\right)^{4} \cdot \left(\frac{1}{6}\right)^{4}$

STEP 6

Calculate the value of the negative one raised to the fourth power.
$\left(-1\right)^{4} = 1$

STEP 7

Calculate the value of one-sixth raised to the fourth power.
$\left(\frac{1}{6}\right)^{4} = \frac{1^4}{6^4}$

STEP 8

Simplify the fraction.
$\frac{1^4}{6^4} = \frac{1}{1296}$

STEP 9

Combine the results from steps 6 and 8.
$\left(-\frac{1}{6}\right)^{4} = 1 \cdot \frac{1}{1296} = \frac{1}{1296}$

STEP 10

Now, we need to multiply the result by 2 as indicated by the expression.
$2 \cdot \frac{1}{1296}$

STEP 11

Perform the multiplication.
$2 \cdot \frac{1}{1296} = \frac{2}{1296}$

STEP 12

Simplify the fraction by dividing both the numerator and the denominator by the greatest common divisor, which is 2.
$\frac{2}{1296} = \frac{1}{648}$

STEP 13

Convert the fraction to a decimal to match the answer choices.
$\frac{1}{648} \approx 0.00154320987654321$

STEP 14

Round the decimal to three significant figures to match the answer choices.
$0.00154320987654321 \approx 0.00154$

STEP 15

Now we compare the result with the answer choices. The closest value to our result is 0.002.
The value equivalent to the expression $2 \cdot(-1 \div 6)^{4}$ is 0.002, which corresponds to answer choice c.

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 2⋅(−1÷6)42 \cdot(-1 \div 6)^{4}2⋅(−1÷6)4 to find the equivalent value.

STEP 1

Assumptions1. The expression to evaluate is 2⋅(−1÷6)42 \cdot(-1 \div 6)^{4}2⋅(−1÷6)4.2. The operations must be performed following the order of operations: parentheses, exponents, multiplication and division from left to right.

STEP 2

First, we need to evaluate the expression inside the parentheses.(−1÷6)(-1 \div 6)(−1÷6)

STEP 3

Perform the division inside the parentheses.(−1÷6)=−16(-1 \div 6) = -\frac{1}{6}(−1÷6)=−61​

STEP 4

Next, we need to raise the result of the division to the power of 4 as indicated by the exponent.(−16)4\left(-\frac{1}{6}\right)^{4}(−61​)4

STEP 5

When raising a negative fraction to an even power, the result is positive. We will raise both the numerator and the denominator to the power of 4.(−16)4=(−1)4⋅(16)4\left(-\frac{1}{6}\right)^{4} = \left(-1\right)^{4} \cdot \left(\frac{1}{6}\right)^{4}(−61​)4=(−1)4⋅(61​)4

STEP 6

Calculate the value of the negative one raised to the fourth power.(−1)4=1\left(-1\right)^{4} = 1(−1)4=1

STEP 7

Calculate the value of one-sixth raised to the fourth power.(16)4=1464\left(\frac{1}{6}\right)^{4} = \frac{1^4}{6^4}(61​)4=6414​

STEP 8

Simplify the fraction.1464=11296\frac{1^4}{6^4} = \frac{1}{1296}6414​=12961​

STEP 9

Combine the results from steps 6 and 8.(−16)4=1⋅11296=11296\left(-\frac{1}{6}\right)^{4} = 1 \cdot \frac{1}{1296} = \frac{1}{1296}(−61​)4=1⋅12961​=12961​

STEP 10

Now, we need to multiply the result by 2 as indicated by the expression.2⋅112962 \cdot \frac{1}{1296}2⋅12961​

STEP 11

Perform the multiplication.2⋅11296=212962 \cdot \frac{1}{1296} = \frac{2}{1296}2⋅12961​=12962​

STEP 12

Simplify the fraction by dividing both the numerator and the denominator by the greatest common divisor, which is 2.21296=1648\frac{2}{1296} = \frac{1}{648}12962​=6481​

STEP 13

Convert the fraction to a decimal to match the answer choices.1648≈0.00154320987654321\frac{1}{648} \approx 0.001543209876543216481​≈0.00154320987654321

STEP 14

Round the decimal to three significant figures to match the answer choices.0.00154320987654321≈0.001540.00154320987654321 \approx 0.001540.00154320987654321≈0.00154

STEP 15

Now we compare the result with the answer choices. The closest value to our result is 0.002.The value equivalent to the expression 2⋅(−1÷6)42 \cdot(-1 \div 6)^{4}2⋅(−1÷6)4 is 0.002, which corresponds to answer choice c.

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 $2 \cdot(-1 \div 6)^{4}$ to find the equivalent value.

Assumptions
1. The expression to evaluate is $2 \cdot(-1 \div 6)^{4}$ .
2. The operations must be performed following the order of operations: parentheses, exponents, multiplication and division from left to right.

First, we need to evaluate the expression inside the parentheses.
$(-1 \div 6)$

Perform the division inside the parentheses.
$(-1 \div 6) = -\frac{1}{6}$

Next, we need to raise the result of the division to the power of 4 as indicated by the exponent.
$\left(-\frac{1}{6}\right)^{4}$

When raising a negative fraction to an even power, the result is positive. We will raise both the numerator and the denominator to the power of 4.
$\left(-\frac{1}{6}\right)^{4} = \left(-1\right)^{4} \cdot \left(\frac{1}{6}\right)^{4}$

Calculate the value of the negative one raised to the fourth power.
$\left(-1\right)^{4} = 1$

Calculate the value of one-sixth raised to the fourth power.
$\left(\frac{1}{6}\right)^{4} = \frac{1^4}{6^4}$

Simplify the fraction.
$\frac{1^4}{6^4} = \frac{1}{1296}$

Combine the results from steps 6 and 8.
$\left(-\frac{1}{6}\right)^{4} = 1 \cdot \frac{1}{1296} = \frac{1}{1296}$

Now, we need to multiply the result by 2 as indicated by the expression.
$2 \cdot \frac{1}{1296}$

Perform the multiplication.
$2 \cdot \frac{1}{1296} = \frac{2}{1296}$

Simplify the fraction by dividing both the numerator and the denominator by the greatest common divisor, which is 2.
$\frac{2}{1296} = \frac{1}{648}$

Convert the fraction to a decimal to match the answer choices.
$\frac{1}{648} \approx 0.00154320987654321$

Round the decimal to three significant figures to match the answer choices.
$0.00154320987654321 \approx 0.00154$

Now we compare the result with the answer choices. The closest value to our result is 0.002.
The value equivalent to the expression $2 \cdot(-1 \div 6)^{4}$ is 0.002, which corresponds to answer choice c.