Solve 30x^10/5x^3

$$\frac { 30 x ^ { 10 } } { 5 x ^ { 3 } }$$

Evaluate

$$6x^{7}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(30x^{10}\right)^{1}\times \frac{1}{5x^{3}}$$

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

$$30^{1}\left(x^{10}\right)^{1}\times \frac{1}{5}\times \frac{1}{x^{3}}$$

Use the Commutative Property of Multiplication.

$$30^{1}\times \frac{1}{5}\left(x^{10}\right)^{1}\times \frac{1}{x^{3}}$$

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

$$30^{1}\times \frac{1}{5}x^{10}x^{3\left(-1\right)}$$

Multiply 3 times -1.

$$30^{1}\times \frac{1}{5}x^{10}x^{-3}$$

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

$$30^{1}\times \frac{1}{5}x^{10-3}$$

Add the exponents 10 and -3.

$$30^{1}\times \frac{1}{5}x^{7}$$

Raise 30 to the power 1.

$$30\times \frac{1}{5}x^{7}$$

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

$$6x^{7}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{30^{1}x^{10}}{5^{1}x^{3}}$$

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

$$\frac{30^{1}x^{10-3}}{5^{1}}$$

Subtract 3 from 10.

$$\frac{30^{1}x^{7}}{5^{1}}$$

Divide 30 by 5.

$$6x^{7}$$

Differentiate w.r.t. x

$$42x^{6}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{30}{5}x^{10-3})$$

Do the arithmetic.

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

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}.

$$7\times 6x^{7-1}$$

Do the arithmetic.

$$42x^{6}$$