2. Find the value of $$ \frac{3 t^{-1}}{t^{\frac{-1}{3}}} $$ (a) $$ \frac{\frac{3}{\frac{2}{2}}}{t^{\frac{3}{3}}} $$ (b) $$ \frac{3}{t^{\frac{3}{2}}} $$ (c) $$ \frac{3}{t^{\frac{1}{3}}} $$ (d) $$ \frac{3}{t^{2}} $$

Question

UpStudy AI · Accepted Answer

To simplify the expression $$ \frac{3 t^{-1}}{t^{\frac{-1}{3}}} $$, let's follow the steps below:

1. **Understand Negative Exponents**:
   - Recall that $$ t^{-a} = \frac{1}{t^{a}} $$.
   - Therefore, $$ t^{-1} = \frac{1}{t} $$ and $$ t^{-\frac{1}{3}} = \frac{1}{t^{\frac{1}{3}}} $$.

2. **Rewrite the Expression**:
   $$
   \frac{3 t^{-1}}{t^{-\frac{1}{3}}} = 3 \cdot \frac{1}{t} \div \frac{1}{t^{\frac{1}{3}}} = 3 \cdot \frac{1}{t} \times t^{\frac{1}{3}} = 3 \cdot t^{-\frac{1}{3}}
   $$

3. **Combine the Exponents**:
   $$
   3 \cdot t^{-\frac{1}{3}} = \frac{3}{t^{\frac{1}{3}}}
   $$

So, the simplified form of the expression is $$ \frac{3}{t^{\frac{1}{3}}} $$.

Among the provided options:

- **(c)** $$ \frac{3}{t^{\frac{1}{3}}} $$ matches our simplified result.

**Answer:**

**(c) $$ \frac{3}{t^{\frac{1}{3}}} $$**
The answer is $$ \frac{3}{t^{\frac{1}{3}}} $$, choice (c).

Find the value of
(a)
(b)
©
(d)

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