Solve (m^-3n)^-2/m^-2n^6

$$\frac { ( m ^ { - 3 } n ) ^ { - 2 } } { m ^ { - 2 } n ^ { 6 } }$$

Evaluate

$$\left(\frac{m}{n}\right)^{8}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(m^{-3}n^{1}\right)^{-2}\times \frac{1}{m^{-2}n^{6}}$$

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

$$\left(m^{-3}\right)^{-2}\left(n^{1}\right)^{-2}\times \frac{1}{m^{-2}}\times \frac{1}{n^{6}}$$

Use the Commutative Property of Multiplication.

$$\left(m^{-3}\right)^{-2}\times \frac{1}{m^{-2}}\left(n^{1}\right)^{-2}\times \frac{1}{n^{6}}$$

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

$$m^{-3\left(-2\right)}m^{-2\left(-1\right)}n^{-2}n^{6\left(-1\right)}$$

Multiply -3 times -2.

$$m^{6}m^{-2\left(-1\right)}n^{-2}n^{6\left(-1\right)}$$

Multiply -2 times -1.

$$m^{6}m^{2}n^{-2}n^{6\left(-1\right)}$$

Multiply 6 times -1.

$$m^{6}m^{2}n^{-2}n^{-6}$$

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

$$m^{6+2}n^{-2-6}$$

Add the exponents 6 and 2.

$$m^{8}n^{-2-6}$$

Add the exponents -2 and -6.

$$m^{8}n^{-8}$$

Expand

$$\left(\frac{m}{n}\right)^{8}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(m^{-3}n^{1}\right)^{-2}\times \frac{1}{m^{-2}n^{6}}$$

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

$$\left(m^{-3}\right)^{-2}\left(n^{1}\right)^{-2}\times \frac{1}{m^{-2}}\times \frac{1}{n^{6}}$$

Use the Commutative Property of Multiplication.

$$\left(m^{-3}\right)^{-2}\times \frac{1}{m^{-2}}\left(n^{1}\right)^{-2}\times \frac{1}{n^{6}}$$

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

$$m^{-3\left(-2\right)}m^{-2\left(-1\right)}n^{-2}n^{6\left(-1\right)}$$

Multiply -3 times -2.

$$m^{6}m^{-2\left(-1\right)}n^{-2}n^{6\left(-1\right)}$$

Multiply -2 times -1.

$$m^{6}m^{2}n^{-2}n^{6\left(-1\right)}$$

Multiply 6 times -1.

$$m^{6}m^{2}n^{-2}n^{-6}$$

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

$$m^{6+2}n^{-2-6}$$

Add the exponents 6 and 2.

$$m^{8}n^{-2-6}$$

Add the exponents -2 and -6.

$$m^{8}n^{-8}$$