Solve 8x^{25}x^{9}z^4quad16x^13y^8z^4

$$8 x ^ { 25 } x ^ { 9 } z ^ { 4 } \quad 16 x ^ { 13 } y ^ { 8 } z ^ { 4 }$$

Evaluate

$$128\left(yz\right)^{8}x^{47}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 25 and 9 to get 34.

$$8x^{34}z^{4}\times 16x^{13}y^{8}z^{4}$$

To multiply powers of the same base, add their exponents. Add 34 and 13 to get 47.

$$8x^{47}z^{4}\times 16y^{8}z^{4}$$

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$8x^{47}z^{8}\times 16y^{8}$$

Multiply 8 and 16 to get 128.

$$128x^{47}z^{8}y^{8}$$

Differentiate w.r.t. x

$$6016\left(yz\right)^{8}x^{46}$$