To solve the expression x to the 1 fourth power times x to the 5 eighths power, we can use the property of exponents that states when you multiply two expressions with the same base, you add the exponents.
The expression can be written as:
x^(1/4) * x^(5/8)
Now, we add the exponents:
1/4 + 5/8
Before adding, we need a common denominator. The least common multiple of 4 and 8 is 8. We convert 1/4 to an equivalent fraction with a denominator of 8:
1/4 = 2/8
Now we can add:
2/8 + 5/8 = 7/8
So, we have:
x^(1/4) * x^(5/8) = x^(7/8)
Therefore, the final answer is:
x to the 7 eighths power.