Solve 8x^-4/2x^-6

$$\frac { 8 x ^ { - 4 } } { 2 x ^ { - 6 } }$$

Evaluate

$$4x^{2}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(8x^{-4}\right)^{1}\times \frac{1}{2x^{-6}}$$

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

$$8^{1}\left(x^{-4}\right)^{1}\times \frac{1}{2}\times \frac{1}{x^{-6}}$$

Use the Commutative Property of Multiplication.

$$8^{1}\times \frac{1}{2}\left(x^{-4}\right)^{1}\times \frac{1}{x^{-6}}$$

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

$$8^{1}\times \frac{1}{2}x^{-4}x^{-6\left(-1\right)}$$

Multiply -6 times -1.

$$8^{1}\times \frac{1}{2}x^{-4}x^{6}$$

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

$$8^{1}\times \frac{1}{2}x^{-4+6}$$

Add the exponents -4 and 6.

$$8^{1}\times \frac{1}{2}x^{2}$$

Raise 8 to the power 1.

$$8\times \frac{1}{2}x^{2}$$

Multiply 8 times \frac{1}{2}.

$$4x^{2}$$

Differentiate w.r.t. x

$$8x$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8}{2}x^{-4-\left(-6\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{2})$$

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}.

$$2\times 4x^{2-1}$$

Do the arithmetic.

$$8x^{1}$$

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

$$8x$$