Solve 7x^3/56x^2

$$\frac { 7 x ^ { 3 } } { 56 x ^ { 2 } }$$

Evaluate

$$\frac{x}{8}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(7x^{3}\right)^{1}\times \frac{1}{56x^{2}}$$

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

$$7^{1}\left(x^{3}\right)^{1}\times \frac{1}{56}\times \frac{1}{x^{2}}$$

Use the Commutative Property of Multiplication.

$$7^{1}\times \frac{1}{56}\left(x^{3}\right)^{1}\times \frac{1}{x^{2}}$$

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

$$7^{1}\times \frac{1}{56}x^{3}x^{2\left(-1\right)}$$

Multiply 2 times -1.

$$7^{1}\times \frac{1}{56}x^{3}x^{-2}$$

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

$$7^{1}\times \frac{1}{56}x^{3-2}$$

Add the exponents 3 and -2.

$$7^{1}\times \frac{1}{56}x^{1}$$

Raise 7 to the power 1.

$$7\times \frac{1}{56}x^{1}$$

Multiply 7 times \frac{1}{56}.

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

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

$$\frac{1}{8}x$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{7^{1}x^{3}}{56^{1}x^{2}}$$

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

$$\frac{7^{1}x^{3-2}}{56^{1}}$$

Subtract 2 from 3.

$$\frac{7^{1}x^{1}}{56^{1}}$$

Reduce the fraction \frac{7}{56} to lowest terms by extracting and canceling out 7.

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

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

$$\frac{1}{8}x$$

Differentiate w.r.t. x

$$\frac{1}{8} = 0.125$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7}{56}x^{3-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{8}x^{1})$$

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}.

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

Do the arithmetic.

$$\frac{1}{8}x^{0}$$

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

$$\frac{1}{8}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{1}{8}$$