Solve frac{(x^{2}y^0)^7}{x^6y^2}

$$\frac { ( x ^ { 2 } y ^ { 0 } ) ^ { 7 } } { x ^ { 6 } y ^ { 2 } }$$

Evaluate

$$\frac{x^{8}}{y^{2}}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(x^{2}y^{0}\right)^{7}\times \frac{1}{x^{6}y^{2}}$$

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

$$\left(x^{2}\right)^{7}\left(y^{0}\right)^{7}\times \frac{1}{x^{6}}\times \frac{1}{y^{2}}$$

Use the Commutative Property of Multiplication.

$$\left(x^{2}\right)^{7}\times \frac{1}{x^{6}}\left(y^{0}\right)^{7}\times \frac{1}{y^{2}}$$

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

$$x^{2\times 7}x^{6\left(-1\right)}y^{0}y^{2\left(-1\right)}$$

Multiply 2 times 7.

$$x^{14}x^{6\left(-1\right)}y^{0}y^{2\left(-1\right)}$$

Multiply 6 times -1.

$$x^{14}x^{-6}y^{0}y^{2\left(-1\right)}$$

Multiply 2 times -1.

$$x^{14}x^{-6}y^{0}y^{-2}$$

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

$$x^{14-6}y^{-2}$$

Add the exponents 14 and -6.

$$x^{8}y^{-2}$$

Expand

$$\frac{x^{8}}{y^{2}}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(x^{2}y^{0}\right)^{7}\times \frac{1}{x^{6}y^{2}}$$

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

$$\left(x^{2}\right)^{7}\left(y^{0}\right)^{7}\times \frac{1}{x^{6}}\times \frac{1}{y^{2}}$$

Use the Commutative Property of Multiplication.

$$\left(x^{2}\right)^{7}\times \frac{1}{x^{6}}\left(y^{0}\right)^{7}\times \frac{1}{y^{2}}$$

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

$$x^{2\times 7}x^{6\left(-1\right)}y^{0}y^{2\left(-1\right)}$$

Multiply 2 times 7.

$$x^{14}x^{6\left(-1\right)}y^{0}y^{2\left(-1\right)}$$

Multiply 6 times -1.

$$x^{14}x^{-6}y^{0}y^{2\left(-1\right)}$$

Multiply 2 times -1.

$$x^{14}x^{-6}y^{0}y^{-2}$$

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

$$x^{14-6}y^{-2}$$

Add the exponents 14 and -6.

$$x^{8}y^{-2}$$