Solve -3^2[-n+5(n-2m)-(n/7)^0]-(m-5n)

$$- 3 ^ { 2 } [ - n + 5 ( n - 2 m ) - ( \frac { n } { 7 } ) ^ { 0 } ] - ( m - 5 n )$$

Evaluate

$$89m-31n+9$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$-9\left(-n+5\left(n-2m\right)-\left(\frac{n}{7}\right)^{0}\right)-\left(m-5n\right)$$

Use the distributive property to multiply 5 by n-2m.

$$-9\left(-n+5n-10m-\left(\frac{n}{7}\right)^{0}\right)-\left(m-5n\right)$$

To raise \frac{n}{7} to a power, raise both numerator and denominator to the power and then divide.

$$-9\left(-n+5n-10m-\frac{n^{0}}{7^{0}}\right)-\left(m-5n\right)$$

Calculate n to the power of 0 and get 1.

$$-9\left(-n+5n-10m-\frac{1}{7^{0}}\right)-\left(m-5n\right)$$

Calculate 7 to the power of 0 and get 1.

$$-9\left(-n+5n-10m-\frac{1}{1}\right)-\left(m-5n\right)$$

Anything divided by one gives itself.

$$-9\left(-n+5n-10m-1\right)-\left(m-5n\right)$$

Use the distributive property to multiply -9 by -n+5n-10m-1.

$$-9\left(-n\right)-45n+90m+9-\left(m-5n\right)$$

Multiply -9 and -1 to get 9.

$$9n-45n+90m+9-\left(m-5n\right)$$

Combine 9n and -45n to get -36n.

$$-36n+90m+9-\left(m-5n\right)$$

To find the opposite of m-5n, find the opposite of each term.

$$-36n+90m+9-m+5n$$

Combine 90m and -m to get 89m.

$$-36n+89m+9+5n$$

Combine -36n and 5n to get -31n.

$$-31n+89m+9$$

Differentiate w.r.t. n

$$-31$$