Solve 56u^7/48u^3

$$\frac { 56 u ^ { 7 } } { 48 u ^ { 3 } }$$

Evaluate

$$\frac{7u^{4}}{6}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(56u^{7}\right)^{1}\times \frac{1}{48u^{3}}$$

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

$$56^{1}\left(u^{7}\right)^{1}\times \frac{1}{48}\times \frac{1}{u^{3}}$$

Use the Commutative Property of Multiplication.

$$56^{1}\times \frac{1}{48}\left(u^{7}\right)^{1}\times \frac{1}{u^{3}}$$

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

$$56^{1}\times \frac{1}{48}u^{7}u^{3\left(-1\right)}$$

Multiply 3 times -1.

$$56^{1}\times \frac{1}{48}u^{7}u^{-3}$$

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

$$56^{1}\times \frac{1}{48}u^{7-3}$$

Add the exponents 7 and -3.

$$56^{1}\times \frac{1}{48}u^{4}$$

Raise 56 to the power 1.

$$56\times \frac{1}{48}u^{4}$$

Multiply 56 times \frac{1}{48}.

$$\frac{7}{6}u^{4}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{56^{1}u^{7}}{48^{1}u^{3}}$$

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

$$\frac{56^{1}u^{7-3}}{48^{1}}$$

Subtract 3 from 7.

$$\frac{56^{1}u^{4}}{48^{1}}$$

Reduce the fraction \frac{56}{48} to lowest terms by extracting and canceling out 8.

$$\frac{7}{6}u^{4}$$

Differentiate w.r.t. u

$$\frac{14u^{3}}{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}u}(\frac{56}{48}u^{7-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}u}(\frac{7}{6}u^{4})$$

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}.

$$4\times \frac{7}{6}u^{4-1}$$

Do the arithmetic.

$$\frac{14}{3}u^{3}$$