Solve 30s^6/5s^4

$$\frac { 30 s ^ { 6 } } { 5 s ^ { 4 } }$$

Evaluate

$$6s^{2}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(30s^{6}\right)^{1}\times \frac{1}{5s^{4}}$$

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

$$30^{1}\left(s^{6}\right)^{1}\times \frac{1}{5}\times \frac{1}{s^{4}}$$

Use the Commutative Property of Multiplication.

$$30^{1}\times \frac{1}{5}\left(s^{6}\right)^{1}\times \frac{1}{s^{4}}$$

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

$$30^{1}\times \frac{1}{5}s^{6}s^{4\left(-1\right)}$$

Multiply 4 times -1.

$$30^{1}\times \frac{1}{5}s^{6}s^{-4}$$

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

$$30^{1}\times \frac{1}{5}s^{6-4}$$

Add the exponents 6 and -4.

$$30^{1}\times \frac{1}{5}s^{2}$$

Raise 30 to the power 1.

$$30\times \frac{1}{5}s^{2}$$

Multiply 30 times \frac{1}{5}.

$$6s^{2}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{30^{1}s^{6}}{5^{1}s^{4}}$$

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

$$\frac{30^{1}s^{6-4}}{5^{1}}$$

Subtract 4 from 6.

$$\frac{30^{1}s^{2}}{5^{1}}$$

Divide 30 by 5.

$$6s^{2}$$

Differentiate w.r.t. s

$$12s$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}s}(\frac{30}{5}s^{6-4})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}s}(6s^{2})$$

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}.

$$2\times 6s^{2-1}$$

Do the arithmetic.

$$12s^{1}$$

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

$$12s$$