$$ \left(\frac{3 b}{a}\right)^{3} $$ as $$ a=2 \operatorname{en} b=-1 $$

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UpStudy AI · Accepted Answer

Evaluate the expression by following steps:
- step0: Evaluate:
  $$\left(\frac{3b}{a}\right)^{3}$$
- step1: Substitute:
  $$\left(\frac{3\left(-1\right)}{2}\right)^{3}$$
- step2: Simplify:
  $$\left(\frac{-3}{2}\right)^{3}$$
- step3: Rewrite the fraction:
  $$\left(-\frac{3}{2}\right)^{3}$$
- step4: Evaluate the power:
  $$-\frac{27}{8}$$
To evaluate the expression $$ \left(\frac{3 b}{a}\right)^{3} $$ with the substitutions $$ a=2 $$ and $$ b=-1 $$, we follow these steps:

1. Substitute the values of $$ a $$ and $$ b $$ into the expression:
   $$
   \left(\frac{3(-1)}{2}\right)^{3}
   $$

2. Simplify the fraction:
   $$
   \left(\frac{-3}{2}\right)^{3}
   $$

3. Calculate the cube of the fraction:
   $$
   \frac{-3^3}{2^3} = \frac{-27}{8}
   $$

Thus, the final result is:
$$
-\frac{27}{8}
$$

This can also be expressed as:
- Mixed number: $$-3\frac{3}{8}$$
- Decimal: $$-3.375$$

You can choose any of these formats based on your preference.
The result of $$ \left(\frac{3 b}{a}\right)^{3} $$ when $$ a=2 $$ and $$ b=-1 $$ is $$-\frac{27}{8}$$ or $$-3.375$$.

\( \left(\frac{3 b}{a}\right)^{3} \) as \( a=2 \operatorname{en} b=-1 \)

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