Solve 16x^6/2x^2

$$\frac { 16 x ^ { 6 } } { 2 x ^ { 2 } }$$

Evaluate

$$8x^{4}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(16x^{6}\right)^{1}\times \frac{1}{2x^{2}}$$

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

$$16^{1}\left(x^{6}\right)^{1}\times \frac{1}{2}\times \frac{1}{x^{2}}$$

Use the Commutative Property of Multiplication.

$$16^{1}\times \frac{1}{2}\left(x^{6}\right)^{1}\times \frac{1}{x^{2}}$$

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

$$16^{1}\times \frac{1}{2}x^{6}x^{2\left(-1\right)}$$

Multiply 2 times -1.

$$16^{1}\times \frac{1}{2}x^{6}x^{-2}$$

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

$$16^{1}\times \frac{1}{2}x^{6-2}$$

Add the exponents 6 and -2.

$$16^{1}\times \frac{1}{2}x^{4}$$

Raise 16 to the power 1.

$$16\times \frac{1}{2}x^{4}$$

Multiply 16 times \frac{1}{2}.

$$8x^{4}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{16^{1}x^{6}}{2^{1}x^{2}}$$

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

$$\frac{16^{1}x^{6-2}}{2^{1}}$$

Subtract 2 from 6.

$$\frac{16^{1}x^{4}}{2^{1}}$$

Divide 16 by 2.

$$8x^{4}$$

Differentiate w.r.t. x

$$32x^{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{16}{2}x^{6-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{4})$$

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}.

$$4\times 8x^{4-1}$$

Do the arithmetic.

$$32x^{3}$$