Solve 8d^4/5d^3

$$\frac { 8 d ^ { 4 } } { 5 d ^ { 3 } }$$

Evaluate

$$\frac{8d}{5}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(8d^{4}\right)^{1}\times \frac{1}{5d^{3}}$$

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

$$8^{1}\left(d^{4}\right)^{1}\times \frac{1}{5}\times \frac{1}{d^{3}}$$

Use the Commutative Property of Multiplication.

$$8^{1}\times \frac{1}{5}\left(d^{4}\right)^{1}\times \frac{1}{d^{3}}$$

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

$$8^{1}\times \frac{1}{5}d^{4}d^{3\left(-1\right)}$$

Multiply 3 times -1.

$$8^{1}\times \frac{1}{5}d^{4}d^{-3}$$

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

$$8^{1}\times \frac{1}{5}d^{4-3}$$

Add the exponents 4 and -3.

$$8^{1}\times \frac{1}{5}d^{1}$$

Raise 8 to the power 1.

$$8\times \frac{1}{5}d^{1}$$

Multiply 8 times \frac{1}{5}.

$$\frac{8}{5}d^{1}$$

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

$$\frac{8}{5}d$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{8^{1}d^{4}}{5^{1}d^{3}}$$

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

$$\frac{8^{1}d^{4-3}}{5^{1}}$$

Subtract 3 from 4.

$$\frac{8^{1}d^{1}}{5^{1}}$$

Divide 8 by 5.

$$\frac{8}{5}d^{1}$$

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

$$\frac{8}{5}d$$

Differentiate w.r.t. d

$$\frac{8}{5} = 1\frac{3}{5} = 1.6$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{8}{5}d^{4-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{8}{5}d^{1})$$

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}.

$$\frac{8}{5}d^{1-1}$$

Do the arithmetic.

$$\frac{8}{5}d^{0}$$

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

$$\frac{8}{5}\times 1$$

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

$$\frac{8}{5}$$