Solve 7*b^5/b^4

$$\frac { 7 \cdot b ^ { 5 } } { b ^ { 4 } }$$

Evaluate

$$7b$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply 4 times -1.

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

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

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

Add the exponents 5 and -4.

$$7^{1}\times \frac{1}{1}b^{1}$$

Raise 7 to the power 1.

$$7\times \frac{1}{1}b^{1}$$

For any term t, t^{1}=t.

$$7\times \frac{1}{1}b$$

Differentiate w.r.t. b

$$7$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{7}{1}b^{5-4})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}b}(7b^{1})$$

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}.

$$7b^{1-1}$$

Do the arithmetic.

$$7b^{0}$$

For any term t except 0, t^{0}=1.

$$7\times 1$$

For any term t, t\times 1=t and 1t=t.

$$7$$