Solve 54b^2c^2/6bc=

$$\frac { 54 b ^ { 2 } c ^ { 2 } } { 6 b c } =$$

Evaluate

$$9bc$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{54^{1}b^{2}c^{2}}{6^{1}b^{1}c^{1}}$$

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

$$\frac{54^{1}}{6^{1}}b^{2-1}c^{2-1}$$

Subtract 1 from 2.

$$\frac{54^{1}}{6^{1}}b^{1}c^{2-1}$$

Subtract 1 from 2.

$$\frac{54^{1}}{6^{1}}bc^{1}$$

Divide 54 by 6.

$$9bc$$

Differentiate w.r.t. b

$$9c$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{54c^{2}}{6c}b^{2-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}b}(9cb^{1})$$

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}.

$$9cb^{1-1}$$

Do the arithmetic.

$$9cb^{0}$$

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

$$9c\times 1$$

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

$$9c$$