Solve 12g^12/6g^6

$$\frac { 12 g ^ { 12 } } { 6 g ^ { 6 } }$$

Evaluate

$$2g^{6}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(12g^{12}\right)^{1}\times \frac{1}{6g^{6}}$$

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

$$12^{1}\left(g^{12}\right)^{1}\times \frac{1}{6}\times \frac{1}{g^{6}}$$

Use the Commutative Property of Multiplication.

$$12^{1}\times \frac{1}{6}\left(g^{12}\right)^{1}\times \frac{1}{g^{6}}$$

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

$$12^{1}\times \frac{1}{6}g^{12}g^{6\left(-1\right)}$$

Multiply 6 times -1.

$$12^{1}\times \frac{1}{6}g^{12}g^{-6}$$

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

$$12^{1}\times \frac{1}{6}g^{12-6}$$

Add the exponents 12 and -6.

$$12^{1}\times \frac{1}{6}g^{6}$$

Raise 12 to the power 1.

$$12\times \frac{1}{6}g^{6}$$

Multiply 12 times \frac{1}{6}.

$$2g^{6}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{12^{1}g^{12}}{6^{1}g^{6}}$$

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

$$\frac{12^{1}g^{12-6}}{6^{1}}$$

Subtract 6 from 12.

$$\frac{12^{1}g^{6}}{6^{1}}$$

Divide 12 by 6.

$$2g^{6}$$

Differentiate w.r.t. g

$$12g^{5}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{12}{6}g^{12-6})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}g}(2g^{6})$$

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}.

$$6\times 2g^{6-1}$$

Do the arithmetic.

$$12g^{5}$$