Solve 35f^7/5f^4

$$\frac { 35 f ^ { 7 } } { 5 f ^ { 4 } }$$

Evaluate

$$7f^{3}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(35f^{7}\right)^{1}\times \frac{1}{5f^{4}}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$35^{1}\left(f^{7}\right)^{1}\times \frac{1}{5}\times \frac{1}{f^{4}}$$

Use the Commutative Property of Multiplication.

$$35^{1}\times \frac{1}{5}\left(f^{7}\right)^{1}\times \frac{1}{f^{4}}$$

To raise a power to another power, multiply the exponents.

$$35^{1}\times \frac{1}{5}f^{7}f^{4\left(-1\right)}$$

Multiply 4 times -1.

$$35^{1}\times \frac{1}{5}f^{7}f^{-4}$$

To multiply powers of the same base, add their exponents.

$$35^{1}\times \frac{1}{5}f^{7-4}$$

Add the exponents 7 and -4.

$$35^{1}\times \frac{1}{5}f^{3}$$

Raise 35 to the power 1.

$$35\times \frac{1}{5}f^{3}$$

Multiply 35 times \frac{1}{5}.

$$7f^{3}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{35^{1}f^{7}}{5^{1}f^{4}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{35^{1}f^{7-4}}{5^{1}}$$

Subtract 4 from 7.

$$\frac{35^{1}f^{3}}{5^{1}}$$

Divide 35 by 5.

$$7f^{3}$$

Differentiate w.r.t. f

$$21f^{2}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}f}(\frac{35}{5}f^{7-4})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}f}(7f^{3})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$3\times 7f^{3-1}$$

Do the arithmetic.

$$21f^{2}$$