Solve 28m^4div7m^15*3m^6

$$28 m ^ { 4 } \div 7 m ^ { 15 } \times 3 m ^ { 6 }$$

Evaluate

$$12m^{25}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 15 and 6 to get 21.

$$\frac{28m^{4}}{7}m^{21}\times 3$$

Divide 28m^{4} by 7 to get 4m^{4}.

$$4m^{4}m^{21}\times 3$$

To multiply powers of the same base, add their exponents. Add 4 and 21 to get 25.

$$4m^{25}\times 3$$

Multiply 4 and 3 to get 12.

$$12m^{25}$$

Differentiate w.r.t. m

$$300m^{24}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 15 and 6 to get 21.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{28m^{4}}{7}m^{21}\times 3)$$

Divide 28m^{4} by 7 to get 4m^{4}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(4m^{4}m^{21}\times 3)$$

To multiply powers of the same base, add their exponents. Add 4 and 21 to get 25.

$$\frac{\mathrm{d}}{\mathrm{d}m}(4m^{25}\times 3)$$

Multiply 4 and 3 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}m}(12m^{25})$$

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

$$25\times 12m^{25-1}$$

Multiply 25 times 12.

$$300m^{25-1}$$

Subtract 1 from 25.

$$300m^{24}$$