Solve 3b^{8}b^-8v^-4v*2x^9*7x^6

$$3 b ^ { 8 } b ^ { - 8 } v ^ { - 4 } v \cdot 2 x ^ { 9 } \cdot 7 x ^ { 6 }$$

Evaluate

$$\frac{42x^{15}}{v^{3}}$$

Solution Steps

Multiply b^{8} and b^{-8} to get 1.

$$3v^{-4}v\times 2x^{9}\times 7x^{6}$$

To multiply powers of the same base, add their exponents. Add -4 and 1 to get -3.

$$3v^{-3}\times 2x^{9}\times 7x^{6}$$

To multiply powers of the same base, add their exponents. Add 9 and 6 to get 15.

$$3v^{-3}\times 2x^{15}\times 7$$

Multiply 3 and 2 to get 6.

$$6v^{-3}x^{15}\times 7$$

Multiply 6 and 7 to get 42.

$$42v^{-3}x^{15}$$

Differentiate w.r.t. x

$$\frac{630x^{14}}{v^{3}}$$