Solve frac{4a^2b^4c^664a^2{b}^3}{4096{a}^4{b}^8{c}^12}

$$\frac{ 4 { a }^{ 2 } { b }^{ 4 } { c }^{ 6 } 64 { a }^{ 2 } { b }^{ 3 } }{ 4096 { a }^{ 4 } { b }^{ 8 } { c }^{ 12 } }$$

Evaluate

$$\frac{1}{16bc^{6}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{4a^{4}b^{4}c^{6}\times 64b^{3}}{4096a^{4}b^{8}c^{12}}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{4a^{4}b^{7}c^{6}\times 64}{4096a^{4}b^{8}c^{12}}$$

Cancel out 4\times 64a^{4}c^{6}b^{7} in both numerator and denominator.

$$\frac{1}{16bc^{6}}$$

Differentiate w.r.t. b

$$-\frac{1}{16b^{2}c^{6}}$$