What is the cube root of 64 in exponential form 64 1/3
The Correct Answer and Explanation is:
The cube root of 64 in exponential form is: 641364^{\frac{1}{3}}6431
Explanation:
The cube root of a number is the value that, when multiplied by itself three times, gives the original number. Mathematically, the cube root of a number xxx is expressed as: x3=x13\sqrt[3]{x} = x^{\frac{1}{3}}3x=x31
In this case, we want to find the cube root of 64. To express this in exponential form, we write: 641364^{\frac{1}{3}}6431
Now, to evaluate 641364^{\frac{1}{3}}6431, we need to break 64 down into its prime factorization: 64=2664 = 2^664=26
This is because 64 can be factored as: 64=2×2×2×2×2×264 = 2 \times 2 \times 2 \times 2 \times 2 \times 264=2×2×2×2×2×2
So we can rewrite the cube root expression as: (26)13(2^6)^{\frac{1}{3}}(26)31
Now, use the exponent rule (am)n=am×n(a^m)^n = a^{m \times n}(am)n=am×n: 26×13=222^{6 \times \frac{1}{3}} = 2^226×31=22
Thus, the cube root of 64 is: 22=42^2 = 422=4
So, the cube root of 64 is 4. The exponential form is 641364^{\frac{1}{3}}6431, and the final result is: 444
