Question
calculate
1 1/3 to the power of 4
1 1/3 to the power of 4
Answers
GPT-4o mini
To calculate \( \left(1 \frac{1}{3}\right)^4 \), first convert the mixed number to an improper fraction.
1. Convert \( 1 \frac{1}{3} \):
\[
1 \frac{1}{3} = \frac{3 \times 1 + 1}{3} = \frac{4}{3}
\]
2. Now, calculate \( \left(\frac{4}{3}\right)^4 \):
\[
\left(\frac{4}{3}\right)^4 = \frac{4^4}{3^4}
\]
3. Calculate \( 4^4 \) and \( 3^4 \):
\[
4^4 = 256 \quad \text{and} \quad 3^4 = 81
\]
4. Therefore,
\[
\left(1 \frac{1}{3}\right)^4 = \frac{256}{81}
\]
So, \( \left(1 \frac{1}{3}\right)^4 = \frac{256}{81} \) or approximately 3.1605.
1. Convert \( 1 \frac{1}{3} \):
\[
1 \frac{1}{3} = \frac{3 \times 1 + 1}{3} = \frac{4}{3}
\]
2. Now, calculate \( \left(\frac{4}{3}\right)^4 \):
\[
\left(\frac{4}{3}\right)^4 = \frac{4^4}{3^4}
\]
3. Calculate \( 4^4 \) and \( 3^4 \):
\[
4^4 = 256 \quad \text{and} \quad 3^4 = 81
\]
4. Therefore,
\[
\left(1 \frac{1}{3}\right)^4 = \frac{256}{81}
\]
So, \( \left(1 \frac{1}{3}\right)^4 = \frac{256}{81} \) or approximately 3.1605.