What is the cube root of 64 in exponential form?
64
3
The Correct Answer and Explanation is:
The cube root of 64 in exponential form is expressed as: 641364^{\frac{1}{3}}6431
Explanation:
To understand this better, let’s break it down step by step:
- Cube Root Definition:
The cube root of a number is a value that, when multiplied by itself three times, gives the original number. Mathematically, for a number xxx, its cube root is written as x3\sqrt[3]{x}3x, which is the same as x13x^{\frac{1}{3}}x31. - Cube Root of 64:
We know that 64=4364 = 4^364=43, which means 4 raised to the power of 3 gives 64: 64=4×4×464 = 4 \times 4 \times 464=4×4×4 Taking the cube root of both sides: 643=433\sqrt[3]{64} = \sqrt[3]{4^3}364=343 Using the property of exponents x33=x\sqrt[3]{x^3} = x3x3=x, we get: 643=4\sqrt[3]{64} = 4364=4 - Exponential Form:
We can express the cube root of 64 as: 6413=(43)13=464^{\frac{1}{3}} = (4^3)^{\frac{1}{3}} = 46431=(43)31=4 So, the cube root of 64 is 4, and in exponential form, it’s written as 641364^{\frac{1}{3}}6431.
To summarize, 643\sqrt[3]{64}364 is equivalent to 641364^{\frac{1}{3}}6431, which simplifies to 4 because 64=4364 = 4^364=43. Therefore, the cube root of 64 in exponential form is 641364^{\frac{1}{3}}6431.
