Solve 3h^4/-3h^-4

$$\frac { 3 h ^ { 4 } } { - 3 h ^ { - 4 } }$$

Evaluate

$$-h^{8}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(3h^{4}\right)^{1}\times \frac{1}{-3h^{-4}}$$

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

$$3^{1}\left(h^{4}\right)^{1}\times \frac{1}{-3}\times \frac{1}{h^{-4}}$$

Use the Commutative Property of Multiplication.

$$3^{1}\times \frac{1}{-3}\left(h^{4}\right)^{1}\times \frac{1}{h^{-4}}$$

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

$$3^{1}\times \frac{1}{-3}h^{4}h^{-4\left(-1\right)}$$

Multiply -4 times -1.

$$3^{1}\times \frac{1}{-3}h^{4}h^{4}$$

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

$$3^{1}\times \frac{1}{-3}h^{4+4}$$

Add the exponents 4 and 4.

$$3^{1}\times \frac{1}{-3}h^{8}$$

Raise 3 to the power 1.

$$3\times \frac{1}{-3}h^{8}$$

Raise -3 to the power -1.

$$3\left(-\frac{1}{3}\right)h^{8}$$

Multiply 3 times -\frac{1}{3}.

$$-h^{8}$$

Differentiate w.r.t. h

$$-8h^{7}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{3}{-3}h^{4-\left(-4\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}h}(-h^{8})$$

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}.

$$8\left(-1\right)h^{8-1}$$

Do the arithmetic.

$$-8h^{7}$$