Solve frac{6*(a^{4})^{7}}{-5}quad(4)frac{(a^{4})^{3}*(a^{5})^{2}}{(a^3)^4*(a^2)^3}

$$\frac { 6 \times ( a ^ { 4 } ) ^ { 7 } } { - 5 } \quad ( 4 ) \frac { ( a ^ { 4 } ) ^ { 3 } \times ( a ^ { 5 } ) ^ { 2 } } { ( a ^ { 3 } ) ^ { 4 } \times ( a ^ { 2 } ) ^ { 3 } }$$

Evaluate

$$-\frac{24a^{32}}{5}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 4 and 7 to get 28.

$$\frac{6a^{28}}{-5}\times 4\times \frac{\left(a^{4}\right)^{3}\left(a^{5}\right)^{2}}{\left(a^{3}\right)^{4}\left(a^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{6a^{28}}{-5}\times 4\times \frac{a^{12}\left(a^{5}\right)^{2}}{\left(a^{3}\right)^{4}\left(a^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{6a^{28}}{-5}\times 4\times \frac{a^{12}a^{10}}{\left(a^{3}\right)^{4}\left(a^{2}\right)^{3}}$$

To multiply powers of the same base, add their exponents. Add 12 and 10 to get 22.

$$\frac{6a^{28}}{-5}\times 4\times \frac{a^{22}}{\left(a^{3}\right)^{4}\left(a^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{6a^{28}}{-5}\times 4\times \frac{a^{22}}{a^{12}\left(a^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{6a^{28}}{-5}\times 4\times \frac{a^{22}}{a^{12}a^{6}}$$

To multiply powers of the same base, add their exponents. Add 12 and 6 to get 18.

$$\frac{6a^{28}}{-5}\times 4\times \frac{a^{22}}{a^{18}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 18 from 22 to get 4.

$$\frac{6a^{28}}{-5}\times 4a^{4}$$

Express \frac{6a^{28}}{-5}\times 4 as a single fraction.

$$\frac{6a^{28}\times 4}{-5}a^{4}$$

Express \frac{6a^{28}\times 4}{-5}a^{4} as a single fraction.

$$\frac{6a^{28}\times 4a^{4}}{-5}$$

To multiply powers of the same base, add their exponents. Add 28 and 4 to get 32.

$$\frac{6a^{32}\times 4}{-5}$$

Multiply 6 and 4 to get 24.

$$\frac{24a^{32}}{-5}$$

Differentiate w.r.t. a

$$-\frac{768a^{31}}{5}$$