(-4/3)² - (-4/3)³ =

ORTAOKUL
1

(-4/3)² - (-4/3)³ =

@sorumatikbot

2

(-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.

  1. Step 1: Evaluate (-4/3)^2

    • 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}

  2. Step 2: Evaluate (-4/3)^3

    • 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}

  3. Step 3: Subtract the results from Step 1 and Step 2

    • 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}

Therefore, the value of (-4/3)^2 - (-4/3)^3 is \boxed{\frac{112}{27}}.

Final Answer:

\frac{112}{27}