Solve 56x^3/-8x^2

$$\frac { 56 x ^ { 3 } } { - 8 x ^ { 2 } }$$

Evaluate

$$-7x$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(56x^{3}\right)^{1}\times \frac{1}{-8x^{2}}$$

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

$$56^{1}\left(x^{3}\right)^{1}\times \frac{1}{-8}\times \frac{1}{x^{2}}$$

Use the Commutative Property of Multiplication.

$$56^{1}\times \frac{1}{-8}\left(x^{3}\right)^{1}\times \frac{1}{x^{2}}$$

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

$$56^{1}\times \frac{1}{-8}x^{3}x^{2\left(-1\right)}$$

Multiply 2 times -1.

$$56^{1}\times \frac{1}{-8}x^{3}x^{-2}$$

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

$$56^{1}\times \frac{1}{-8}x^{3-2}$$

Add the exponents 3 and -2.

$$56^{1}\times \frac{1}{-8}x^{1}$$

Raise 56 to the power 1.

$$56\times \frac{1}{-8}x^{1}$$

Raise -8 to the power -1.

$$56\left(-\frac{1}{8}\right)x^{1}$$

Multiply 56 times -\frac{1}{8}.

$$-7x^{1}$$

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

$$-7x$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{56^{1}x^{3}}{\left(-8\right)^{1}x^{2}}$$

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

$$\frac{56^{1}x^{3-2}}{\left(-8\right)^{1}}$$

Subtract 2 from 3.

$$\frac{56^{1}x^{1}}{\left(-8\right)^{1}}$$

Divide 56 by -8.

$$-7x^{1}$$

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

$$-7x$$

Differentiate w.r.t. x

$$-7$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{56}{-8}x^{3-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-7x^{1})$$

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}.

$$-7x^{1-1}$$

Do the arithmetic.

$$-7x^{0}$$

For any term t except 0, t^{0}=1.

$$-7$$