Final answer:
To simplify the expression (5x^-3 + 7x + 6)^5/2, start by simplifying the exponent 5/2 to the square root of 5 raised to the power of 2. Distribute this exponent to each term inside the parentheses, and then simplify each term using the power rule. The final simplified expression is 5^-15 + 49x + 6^5.
Step-by-step explanation:
To simplify the expression (5x-3 + 7x + 6)5/2, we can start by simplifying the exponent 5/2. The exponent 5/2 can be written as the square root of 5 raised to the power of 2. So, (5x-3 + 7x + 6)5/2 becomes (5x-3 + 7x + 6)√52.
Next, we can distribute the exponent of 2 to each term inside the parentheses. (5x-3)√52 + (7x)√52 + (6)√52.
Finally, we can simplify each term using the rule that (ab)c = ab*c. This gives us 5-3√52 + 7√52x + 6√52. And simplifying further, we have 5-15 + 49x + 65 as the simplified expression.