How do I solve this:
((5m^3)(3m^-1)^3)/((9n^2)(4n^-1))?
You have two variables (m and n) and one algebraic expression that is not even an equation. There is no solution. It is just a formula.
Did you mean to have the same variable (m or n) in the numerator and denominator? In that case, some simplification would be possible.
6910 divide by 4
1727.5
To solve the given expression, follow these steps:
Step 1: Simplify the exponents within the parentheses.
- In the numerator, simplify (3m^-1)^3 by raising both the base (3m^-1) and the exponent (3) to the power of 3. This results in (3^3)(m^-1)^3 = 27m^-3.
- In the denominator, simplify (4n^-1) by raising both the base (4n^-1) and the exponent (1) to the power of -1. This results in 4n.
Step 2: Substitute the simplified expressions back into the original equation.
- The expression now becomes ((5m^3)(27m^-3))/((9n^2)(4n)).
Step 3: Further simplify and solve.
- In the numerator, multiply the coefficients (5)(27) to get 135.
- In the denominator, multiply the coefficients (9)(4) to get 36.
- Simplify the variables by subtracting the exponents: m^3/m^-3 = m^(3-(-3)) = m^6.
- Simplify the variables by subtracting the exponents: n^2/n = n^(2-1) = n^1 = n.
Step 4: Combine all parts of the expression for the final answer.
- The simplified expression is 135m^6/36n.
Therefore, the solution to the given expression is 135m^6/36n.