Question

Evaluate: 6-(2/3)^2A. 17/3B. 52/3C. 49/9D. 50/9​

Answer 1

Answer:

The correct answer is: "Option [D]".

Step-by-step explanation:

Hi student, let me help you out!

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Let's use the acronym PEMDAS. With the help of this little acronym, we will not make mistakes in the Order of Operations!  :)

$\dag\textsf{Acronym \: PEMDAS}$

P=Parentheses,

E=Exponents,

M=Multiplication,

D=Division,

A=Addition,

S=Subtraction.

Now let's start evaluating our expression, which is $\mathsf{6-(\cfrac{2}{3})^2}$

According to PEMDAS, the operation that we should perform is "E-Exponents".

Notice that we have a fraction raised to a power. When this happens, we raise both the numerator (2 in this case) and the denominator (3 in this case) to that power, which is 2. After this we obtain  $\mathsf{6-\cfrac{4}{9}}$.

See, we raised both the numerator and the denominator to the power of 2.

Now what we should do is subtract fractions.

Note that 6 and -4/9 have unlike denominators. First, let's write 6 as a fraction: $\mathrm{\cfrac{6}{1}-\cfrac{4}{9}}$. Now let's multiply the denominator and the numerator of the first fraction times 9: $\mathrm{\cfrac{54}{9}-\cfrac{4}{9}}$.

See, now the fractions have the same denominator. All we should do now is subtract the numerators: $\mathrm{\cfrac{50}{9}}$.

∴, the answer is Option D.

Hope this helped you out, ask in comments if any queries arise.

Best Wishes!

$\star\bigstar\underline{\overline{\overline{\underline{\textsf{Reach \: far. Aim \: high. Dream \: big.}}}}}\bigstar\star$

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Answer 2

Calculate 2/3, to the power of 3, therefore

$\bf{\left(\dfrac{2}{3}\right)^{2}=\dfrac{2\times2}{3\times3}=\dfrac{4}{9} }$

$\bf{6-\dfrac{4}{9} }$

Convert 6 to the fraction 54/9.

$\bf{\dfrac{54}{9}-\dfrac{4}{9} }$

Since 54/9 and 4/9 have the same denominator, join their numerators to subtract them.

$\bf{\dfrac{54-4}{9} \ \ \to \ \ \ Subtract }$

Subtract 4 from 54 to get 50.

$\bf{\dfrac{50}{9} \ \ \to \ \ \ Answer }$

Therefore, the correct alternative is "D".

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