Solve 7a^12div56a^15

$$7 a ^ { 12 } \div 56 a ^ { 15 }$$

Evaluate

$$\frac{a^{27}}{8}$$

Solution Steps

Divide 7a^{12} by 56 to get \frac{1}{8}a^{12}.

$$\frac{1}{8}a^{12}a^{15}$$

To multiply powers of the same base, add their exponents. Add 12 and 15 to get 27.

$$\frac{1}{8}a^{27}$$

Differentiate w.r.t. a

$$\frac{27a^{26}}{8}$$

Steps Using Definition of a Derivative

Divide 7a^{12} by 56 to get \frac{1}{8}a^{12}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{8}a^{12}a^{15})$$

To multiply powers of the same base, add their exponents. Add 12 and 15 to get 27.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{8}a^{27})$$

The derivative of ax^{n} is nax^{n-1}.

$$27\times \frac{1}{8}a^{27-1}$$

Multiply 27 times \frac{1}{8}.

$$\frac{27}{8}a^{27-1}$$

Subtract 1 from 27.

$$\frac{27}{8}a^{26}$$