Solve b^97:b^6

$$b ^ { 97 } : b ^ { 6 }$$

Evaluate

$$b^{91}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{b^{97}}{b^{6}}$$

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

$$b^{97-6}$$

Subtract 6 from 97.

$$b^{91}$$

Differentiate w.r.t. b

$$91b^{90}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{1}{1}b^{97-6})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b^{91})$$

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}.

$$91b^{91-1}$$

Do the arithmetic.

$$91b^{90}$$