Final answer:
To express ^7 sqrt (10x)^4 in rational exponent form, we convert the seventh root into an exponent, resulting in the expression (10x)^(4/7).
Step-by-step explanation:
To write ^7 sqrt (10x)^4 in rational exponent form, we can use the properties of exponents and radicals.
The expression given is the seventh root of (10x) raised to the fourth power.
We can translate this root expression into exponent form by recognizing that taking the seventh root is the same as raising the expression to the power of 1/7.
Using this knowledge, (10x)^4 under a seventh root is the same as (10x) raised to the power of 4/7 when expressed with a rational exponent.
Therefore, our expression in rational exponent form becomes (10x)^(4/7).