Solve 8w^13/w^7=

$$\frac { 8 w ^ { 13 } } { w ^ { 7 } } =$$

Evaluate

$$8w^{6}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(8w^{13}\right)^{1}\times \frac{1}{w^{7}}$$

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

$$8^{1}\left(w^{13}\right)^{1}\times \frac{1}{1}\times \frac{1}{w^{7}}$$

Use the Commutative Property of Multiplication.

$$8^{1}\times \frac{1}{1}\left(w^{13}\right)^{1}\times \frac{1}{w^{7}}$$

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

$$8^{1}\times \frac{1}{1}w^{13}w^{7\left(-1\right)}$$

Multiply 7 times -1.

$$8^{1}\times \frac{1}{1}w^{13}w^{-7}$$

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

$$8^{1}\times \frac{1}{1}w^{13-7}$$

Add the exponents 13 and -7.

$$8^{1}\times \frac{1}{1}w^{6}$$

Raise 8 to the power 1.

$$8\times \frac{1}{1}w^{6}$$

Differentiate w.r.t. w

$$48w^{5}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{8}{1}w^{13-7})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}w}(8w^{6})$$

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}.

$$6\times 8w^{6-1}$$

Do the arithmetic.

$$48w^{5}$$