Questions: Write -(-243)^(1/5) using exponents and evaluate -(-243)^(1/5) using exponents is written as (Use positive exponents only. Do not simplify. Use integers or fractions numbers in the expression.)

Solution Steps

To solve the problem of writing \( -\sqrt[5]{-243} \) using exponents and evaluating it, we can follow these steps:

1. Recognize that the expression \( -\sqrt[5]{-243} \) can be rewritten using exponents.
2. The fifth root of a number \( x \) can be expressed as \( x^{1/5} \).
3. Therefore, \( -\sqrt[5]{-243} \) can be written as \( -(-243)^{1/5} \).
4. Evaluate the expression \( (-243)^{1/5} \).

The given expression is \( -\sqrt[5]{-243} \). We can rewrite the fifth root using exponents: \[ -\sqrt[5]{-243} = -(-243)^{1/5} \]

To evaluate \( (-243)^{1/5} \), we recognize that: \[ (-243)^{1/5} = -3 \] Thus: \[ -(-243)^{1/5} = -(-3) = 3 \]

Final Answer