Solve 8x^2/4x^-4

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

Evaluate

$$2x^{6}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply -4 times -1.

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

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

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

Add the exponents 2 and 4.

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

Raise 8 to the power 1.

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

Multiply 8 times \frac{1}{4}.

$$2x^{6}$$

Differentiate w.r.t. x

$$12x^{5}$$

Solution Steps

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

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

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$12x^{5}$$