2^0.4
Understand the Problem
The question asks to evaluate the expression 2^0.4. This involves calculating 2 raised to the power of 0.4.
Answer
$\sqrt[5]{4} \approx 1.3195$
Answer for screen readers
$\sqrt[5]{4} \approx 1.3195$
Steps to Solve
- Rewrite the exponent as a fraction
Convert the decimal exponent 0.4 to a fraction.
$0.4 = \frac{4}{10} = \frac{2}{5}$
- Rewrite the expression with the fractional exponent
Replace 0.4 with $\frac{2}{5}$ in the original expression.
$2^{0.4} = 2^{\frac{2}{5}}$
- Rewrite the expression using radicals
Use the property $a^{\frac{m}{n}} = \sqrt[n]{a^m}$ to rewrite the expression with a radical.
$2^{\frac{2}{5}} = \sqrt[5]{2^2}$
- Simplify the expression
Evaluate $2^2$ to simplify the expression inside the radical.
$\sqrt[5]{2^2} = \sqrt[5]{4}$
- Approximate the value (if needed)
The problem does not directly mention if an approximation is required. However $\sqrt[5]{4}$ is the simplest exact form. If approximation is needed, we can approximate, typically rounded to a few decimal places using a calculator:
$\sqrt[5]{4} \approx 1.3195$
$\sqrt[5]{4} \approx 1.3195$
More Information
The expression $2^{0.4}$ can be represented exactly as $\sqrt[5]{4}$. The approximate decimal value is around 1.3195.
Tips
A common mistake is incorrectly converting the decimal to a fraction. Another common mistake involves misinterpreting fractional exponents and radicals.
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