$$ \frac{1}{3}\left(3 x^{2} y^{-3}\right)^{2} $$ as $$ x=2 $$ en $$ y=-1 $$

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UpStudy AI · Accepted Answer

Evaluate the expression by following steps:
- step0: Evaluate:
  $$\frac{1}{3}\left(3x^{2}y^{-3}\right)^{2}$$
- step1: Substitute:
  $$\frac{1}{3}\left(3\times 2^{2}\left(-1\right)^{-3}\right)^{2}$$
- step2: Multiply the terms:
  $$\frac{1}{3}\left(-12\right)^{2}$$
- step3: Rewrite the expression:
  $$\frac{1}{3}\times 3^{2}\left(-4\right)^{2}$$
- step4: Reduce the numbers:
  $$1\times 3\left(-4\right)^{2}$$
- step5: Simplify:
  $$48$$
To evaluate the expression $$ \frac{1}{3}\left(3 x^{2} y^{-3}\right)^{2} $$ with the substitutions $$ x=2 $$ and $$ y=-1 $$, we follow these steps:

1. Substitute $$ x $$ and $$ y $$ into the expression:
   $$
   \frac{1}{3}\left(3 (2)^{2} (-1)^{-3}\right)^{2}
   $$

2. Calculate $$ (2)^{2} $$:
   $$
   (2)^{2} = 4
   $$

3. Calculate $$ (-1)^{-3} $$:
   $$
   (-1)^{-3} = -1
   $$

4. Substitute these values back into the expression:
   $$
   \frac{1}{3}\left(3 \cdot 4 \cdot (-1)\right)^{2}
   $$

5. Calculate $$ 3 \cdot 4 \cdot (-1) $$:
   $$
   3 \cdot 4 \cdot (-1) = -12
   $$

6. Now, square $$-12$$:
   $$
   (-12)^{2} = 144
   $$

7. Finally, multiply by $$ \frac{1}{3} $$:
   $$
   \frac{1}{3} \cdot 144 = 48
   $$

Thus, the final result is $$ 48 $$.
The result is 48.

\( \frac{1}{3}\left(3 x^{2} y^{-3}\right)^{2} \) as \( x=2 \) en \( y=-1 \)

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