Solve 34z^17/10z^7

$$\frac { 34 z ^ { 17 } } { 10 z ^ { 7 } }$$

Evaluate

$$\frac{17z^{10}}{5}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(34z^{17}\right)^{1}\times \frac{1}{10z^{7}}$$

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

$$34^{1}\left(z^{17}\right)^{1}\times \frac{1}{10}\times \frac{1}{z^{7}}$$

Use the Commutative Property of Multiplication.

$$34^{1}\times \frac{1}{10}\left(z^{17}\right)^{1}\times \frac{1}{z^{7}}$$

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

$$34^{1}\times \frac{1}{10}z^{17}z^{7\left(-1\right)}$$

Multiply 7 times -1.

$$34^{1}\times \frac{1}{10}z^{17}z^{-7}$$

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

$$34^{1}\times \frac{1}{10}z^{17-7}$$

Add the exponents 17 and -7.

$$34^{1}\times \frac{1}{10}z^{10}$$

Raise 34 to the power 1.

$$34\times \frac{1}{10}z^{10}$$

Multiply 34 times \frac{1}{10}.

$$\frac{17}{5}z^{10}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{34^{1}z^{17}}{10^{1}z^{7}}$$

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

$$\frac{34^{1}z^{17-7}}{10^{1}}$$

Subtract 7 from 17.

$$\frac{34^{1}z^{10}}{10^{1}}$$

Reduce the fraction \frac{34}{10} to lowest terms by extracting and canceling out 2.

$$\frac{17}{5}z^{10}$$

Differentiate w.r.t. z

$$34z^{9}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{34}{10}z^{17-7})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{17}{5}z^{10})$$

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}.

$$10\times \frac{17}{5}z^{10-1}$$

Do the arithmetic.

$$34z^{9}$$