Final answer:
To convert the expression √x³y²z⁵ into exponential form, we represent the square root as a fractional exponent of ½ and multiply it with the current exponents, resulting in x³/²y¹/²z⁵/². The correct answer is option b, which is x³/²y¹/²z⁵/².
Step-by-step explanation:
The student's question asks which option represents the exponential form of √x³y²z⁵. To solve this, we need to express the square root in exponential terms. Recall that the square root of any number or expression can be represented as a fractional exponent of ½. Therefore, if we have the expression √x³y²z⁵, the exponential form would involve every variable being raised to the power of ½ which is multiplied with their current exponents. So:
- √x³ will be x to the power of 3/2 or x³/²
- √y² will be y to the power of 2/2 or y¹/²
- √z⁵ will be z to the power of 5/2 or z⁵/²
Combining these, we get the expression x³/²y¹/²z⁵/². Therefore, the correct answer is option b, which is x³/²y¹/²z⁵/².
This approach relies on an understanding of the laws of exponents outlined in previous materials, such as how to multiply exponential terms and convert square roots into fractional powers.