Final answer:
The expression 7tu⁸vw/7t³u⁴vw simplifies to t⁵u⁴ after canceling out similar terms and applying the division of exponentials rule.
Step-by-step explanation:
To simplify the expression 7tu⁸vw/7t³u⁴vw, we start by eliminating terms that are the same in both the numerator and denominator.
- The '7' in the numerator and denominator cancel out.
- The variable 't' has a higher power in the denominator (t³) than in the numerator (t), so we subtract the exponent in the denominator from the exponent in the numerator resulting in t¸ - t³ = t⁵.
- For the variable 'u', we again subtract the exponent in the denominator (u⁴) from the exponent in the numerator (u⁸) giving us u⁴.
- The variables 'v' and 'w' cancel out as they have the same exponent in both the numerator and the denominator.
This leads to the simplified result of t⁵u⁴.
To check if it is reasonable, we review the steps to ensure that we have correctly applied the division of exponentials.