Solve 7s^6/7s^-7

$$\frac { 7 s ^ { 6 } } { 7 s ^ { - 7 } }$$

Evaluate

$$s^{13}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(7s^{6}\right)^{1}\times \frac{1}{7s^{-7}}$$

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

$$7^{1}\left(s^{6}\right)^{1}\times \frac{1}{7}\times \frac{1}{s^{-7}}$$

Use the Commutative Property of Multiplication.

$$7^{1}\times \frac{1}{7}\left(s^{6}\right)^{1}\times \frac{1}{s^{-7}}$$

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

$$7^{1}\times \frac{1}{7}s^{6}s^{-7\left(-1\right)}$$

Multiply -7 times -1.

$$7^{1}\times \frac{1}{7}s^{6}s^{7}$$

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

$$7^{1}\times \frac{1}{7}s^{6+7}$$

Add the exponents 6 and 7.

$$7^{1}\times \frac{1}{7}s^{13}$$

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

$$7^{1-1}s^{13}$$

Add the exponents 1 and -1.

$$7^{0}s^{13}$$

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

$$1s^{13}$$

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

$$s^{13}$$

Differentiate w.r.t. s

$$13s^{12}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}s}(\frac{7}{7}s^{6-\left(-7\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}s}(s^{13})$$

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}.

$$13s^{13-1}$$

Do the arithmetic.

$$13s^{12}$$