Solve (m^6n)^-3/m^-7n^5

$$\frac { ( m ^ { 6 } n ) ^ { - 3 } } { m ^ { - 7 } n ^ { 5 } }$$

Evaluate

$$\frac{1}{n^{8}m^{11}}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(m^{6}n^{1}\right)^{-3}\times \frac{1}{m^{-7}n^{5}}$$

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

$$\left(m^{6}\right)^{-3}\left(n^{1}\right)^{-3}\times \frac{1}{m^{-7}}\times \frac{1}{n^{5}}$$

Use the Commutative Property of Multiplication.

$$\left(m^{6}\right)^{-3}\times \frac{1}{m^{-7}}\left(n^{1}\right)^{-3}\times \frac{1}{n^{5}}$$

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

$$m^{6\left(-3\right)}m^{-7\left(-1\right)}n^{-3}n^{5\left(-1\right)}$$

Multiply 6 times -3.

$$m^{-18}m^{-7\left(-1\right)}n^{-3}n^{5\left(-1\right)}$$

Multiply -7 times -1.

$$m^{-18}m^{7}n^{-3}n^{5\left(-1\right)}$$

Multiply 5 times -1.

$$m^{-18}m^{7}n^{-3}n^{-5}$$

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

$$m^{-18+7}n^{-3-5}$$

Add the exponents -18 and 7.

$$m^{-11}n^{-3-5}$$

Add the exponents -3 and -5.

$$m^{-11}n^{-8}$$

Expand

$$\frac{1}{n^{8}m^{11}}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(m^{6}n^{1}\right)^{-3}\times \frac{1}{m^{-7}n^{5}}$$

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

$$\left(m^{6}\right)^{-3}\left(n^{1}\right)^{-3}\times \frac{1}{m^{-7}}\times \frac{1}{n^{5}}$$

Use the Commutative Property of Multiplication.

$$\left(m^{6}\right)^{-3}\times \frac{1}{m^{-7}}\left(n^{1}\right)^{-3}\times \frac{1}{n^{5}}$$

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

$$m^{6\left(-3\right)}m^{-7\left(-1\right)}n^{-3}n^{5\left(-1\right)}$$

Multiply 6 times -3.

$$m^{-18}m^{-7\left(-1\right)}n^{-3}n^{5\left(-1\right)}$$

Multiply -7 times -1.

$$m^{-18}m^{7}n^{-3}n^{5\left(-1\right)}$$

Multiply 5 times -1.

$$m^{-18}m^{7}n^{-3}n^{-5}$$

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

$$m^{-18+7}n^{-3-5}$$

Add the exponents -18 and 7.

$$m^{-11}n^{-3-5}$$

Add the exponents -3 and -5.

$$m^{-11}n^{-8}$$