Questions: 64^(1/3) use rational exponents to put this in different form

Solution Steps

To solve \(64^{\frac{1}{3}}\) using rational exponents, we need to recognize that this expression represents the cube root of 64. We can rewrite the expression in a different form by finding the cube root of 64.

We start with the expression \(64^{\frac{1}{3}}\). This can be interpreted as the cube root of 64, which can be expressed mathematically as: \[ \sqrt[3]{64} \]

Next, we calculate the cube root of 64. Since \(64 = 4^3\), we can simplify: \[ \sqrt[3]{64} = \sqrt[3]{4^3} = 4 \]

The result of the calculation shows that \(64^{\frac{1}{3}} \approx 3.9999999999999996\). Rounding this to four significant digits gives us: \[ 4.000 \]

Final Answer