Final Answer:
The quantity
can be transformed into an expression with a rational exponent by applying the properties of exponents and simplifying the radicals:
![[(5√(x) )^7]^3 = (5^7)(x^((7/2)))^3 = 5^21 * x^((21/2))](https://img.qammunity.org/2023/formulas/mathematics/college/m24og4l4m1ksqddhs9q4sh60nfniushjaw.png)
Step-by-step explanation:
Apply the power of a power rule: We can start by breaking down the expression inside the parentheses:
![[(5√(x) )^7]^3 = (5^((7/2)))^3](https://img.qammunity.org/2023/formulas/mathematics/college/n9tl0ki7m06d8rh6a6a5881bs8m5te7fzp.png)
Simplify the radicals: Since we have a power of another power, we can simplify the radical:

Combine exponents with the same base: Now we can combine the exponents with the same base:

Therefore, the transformed expression with a rational exponent is
