(-4/3)² - (-4/3)³ =
(-4/3)² - (-4/3)³ = ?
Answer:
To determine the value of the expression (-4/3)^2 - (-4/3)^3, we’ll evaluate each term separately and then subtract the results.
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Step 1: Evaluate (-4/3)^2
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The exponentiation of (-4/3)^2 can be calculated as follows:
\left(\frac{-4}{3}\right)^2 = \frac{(-4)^2}{3^2} = \frac{16}{9}
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Step 2: Evaluate (-4/3)^3
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The exponentiation of (-4/3)^3 can be calculated as follows:
\left(\frac{-4}{3}\right)^3 = \frac{(-4)^3}{3^3} = \frac{-64}{27}
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Step 3: Subtract the results from Step 1 and Step 2
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Now, subtract the result of (-4/3)^3 from (-4/3)^2:
\frac{16}{9} - \left(\frac{-64}{27}\right) -
To subtract these fractions, we need a common denominator. The least common multiple (LCM) of 9 and 27 is 27. Convert \frac{16}{9} to \frac{48}{27}:
\frac{16}{9} = \frac{16 \times 3}{9 \times 3} = \frac{48}{27} -
Now, subtract the fractions using the common denominator:
\frac{48}{27} - \left(\frac{-64}{27}\right) = \frac{48}{27} + \frac{64}{27} = \frac{48 + 64}{27} = \frac{112}{27}
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Therefore, the value of (-4/3)^2 - (-4/3)^3 is \boxed{\frac{112}{27}}.
Final Answer:
\frac{112}{27}