Solve 9m^{8}n^0*8mn^3*8m^-7n^0

$$9 m ^ { 8 } n ^ { 0 } \cdot 8 m n ^ { 3 } \cdot 8 m ^ { - 7 } n ^ { 0 }$$

Evaluate

$$576m^{2}n^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 8 and 1 to get 9.

$$9m^{9}n^{0}\times 8n^{3}\times 8m^{-7}n^{0}$$

To multiply powers of the same base, add their exponents. Add 9 and -7 to get 2.

$$9m^{2}n^{0}\times 8n^{3}\times 8n^{0}$$

To multiply powers of the same base, add their exponents. Add 0 and 3 to get 3.

$$9m^{2}n^{3}\times 8\times 8n^{0}$$

To multiply powers of the same base, add their exponents. Add 3 and 0 to get 3.

$$9m^{2}n^{3}\times 8\times 8$$

Multiply 9 and 8 to get 72.

$$72m^{2}n^{3}\times 8$$

Multiply 72 and 8 to get 576.

$$576m^{2}n^{3}$$

Differentiate w.r.t. n

$$1728\left(mn\right)^{2}$$