Question

Evaluate:

6-(2/3)^2

A. 17/3
B. 52/3
C. 49/9
D. 50/9​

Answer 1

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

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`

`\underline{\rule{300}{5}}`

Answer 2

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

`\bf{\left((2)/(3)\right)^(2)=(2*2)/(3*3)=(4)/(9) }`

`\bf{6-(4)/(9) }`

Convert 6 to the fraction 54/9.

`\bf{(54)/(9)-(4)/(9) }`

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

`\bf{(54-4)/(9) \ \ \to \ \ \ Subtract }`

Subtract 4 from 54 to get 50.

`\bf{(50)/(9) \ \ \to \ \ \ Answer }`

Therefore, the correct alternative is "D".

`\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}`