Solve 49y^6/56y^2

$$\frac { 49 y ^ { 6 } } { 56 y ^ { 2 } }$$

Evaluate

$$\frac{7y^{4}}{8}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(49y^{6}\right)^{1}\times \frac{1}{56y^{2}}$$

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

$$49^{1}\left(y^{6}\right)^{1}\times \frac{1}{56}\times \frac{1}{y^{2}}$$

Use the Commutative Property of Multiplication.

$$49^{1}\times \frac{1}{56}\left(y^{6}\right)^{1}\times \frac{1}{y^{2}}$$

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

$$49^{1}\times \frac{1}{56}y^{6}y^{2\left(-1\right)}$$

Multiply 2 times -1.

$$49^{1}\times \frac{1}{56}y^{6}y^{-2}$$

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

$$49^{1}\times \frac{1}{56}y^{6-2}$$

Add the exponents 6 and -2.

$$49^{1}\times \frac{1}{56}y^{4}$$

Raise 49 to the power 1.

$$49\times \frac{1}{56}y^{4}$$

Multiply 49 times \frac{1}{56}.

$$\frac{7}{8}y^{4}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{49^{1}y^{6}}{56^{1}y^{2}}$$

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

$$\frac{49^{1}y^{6-2}}{56^{1}}$$

Subtract 2 from 6.

$$\frac{49^{1}y^{4}}{56^{1}}$$

Reduce the fraction \frac{49}{56} to lowest terms by extracting and canceling out 7.

$$\frac{7}{8}y^{4}$$

Differentiate w.r.t. y

$$\frac{7y^{3}}{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{49}{56}y^{6-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{7}{8}y^{4})$$

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}.

$$4\times \frac{7}{8}y^{4-1}$$

Do the arithmetic.

$$\frac{7}{2}y^{3}$$