answer:
To simplify the expression (m^2/5n^1/2)^5/2, we can follow these steps:
1. Simplify the exponents inside the parentheses:
- The exponent of m^2 becomes m^(2*(5/2)), which simplifies to m^5.
- The exponent of 5n^(1/2) becomes (5/2)*(1/2), which simplifies to 5/4.
2. Rewrite the expression with the simplified exponents:
(m^5/(5n^(1/4)))^5/2
3. Apply the exponent outside the parentheses to both the numerator and the denominator:
m^(5*(5/2))/(5^(5/2)*n^(5/4))
4. Simplify the exponents:
m^(5/2)/(5^(5/2)*n^(5/4))
5. Rewrite 5^(5/2) as the square root of 5 raised to the power of 5:
m^(5/2)/(√5^5*n^(5/4))
6. Simplify the square root of 5 raised to the power of 5:
m^(5/2)/(√3125*n^(5/4))
7. Simplify √3125 to 5√5:
m^(5/2)/(5√5*n^(5/4))
Therefore, the simplified expression is m^(5/2)/(5√5*n^(5/4))
the silly