Questions: (-2/3)^2

(-2/3)^2
Transcript text: $\left(-\frac{2}{3}\right)^{2}$
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Solution

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Solution Steps

Step 1: Squaring the Numerator and Denominator

To evaluate (23)2\left(-\frac{2}{3}\right)^{2}, we first square the numerator and the denominator separately. The numerator is 2-2, and squaring it gives: (2)2=4 (-2)^{2} = 4 The denominator is 33, and squaring it gives: 32=9 3^{2} = 9

Step 2: Forming the Squared Fraction

Now, we can form the squared fraction using the squared numerator and denominator: (23)2=49 \left(-\frac{2}{3}\right)^{2} = \frac{4}{9}

Step 3: Decimal Representation

The decimal representation of 49\frac{4}{9} is approximately 0.44440.4444 when rounded to four significant digits.

Final Answer

Thus, the final result of the expression (23)2\left(-\frac{2}{3}\right)^{2} is: 49 \boxed{\frac{4}{9}}

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