Solve {left(-3m^5n^4/n^2right)}^5div27m^8{n}^9

$${ \left(- \frac{ 3 { m }^{ 5 } { n }^{ 4 } }{ { n }^{ 2 } } \right) }^{ 5 } \div 27 { m }^{ 8 } { n }^{ 9 }$$

Evaluate

$$-9n^{19}m^{33}$$

Solution Steps

Cancel out n^{2} in both numerator and denominator.

$$\frac{\left(-3n^{2}m^{5}\right)^{5}}{27}m^{8}n^{9}$$

Express \frac{\left(-3n^{2}m^{5}\right)^{5}}{27}m^{8} as a single fraction.

$$\frac{\left(-3n^{2}m^{5}\right)^{5}m^{8}}{27}n^{9}$$

Express \frac{\left(-3n^{2}m^{5}\right)^{5}m^{8}}{27}n^{9} as a single fraction.

$$\frac{\left(-3n^{2}m^{5}\right)^{5}m^{8}n^{9}}{27}$$

Expand \left(-3n^{2}m^{5}\right)^{5}.

$$\frac{\left(-3\right)^{5}\left(n^{2}\right)^{5}\left(m^{5}\right)^{5}m^{8}n^{9}}{27}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\frac{\left(-3\right)^{5}n^{10}\left(m^{5}\right)^{5}m^{8}n^{9}}{27}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 5 to get 25.

$$\frac{\left(-3\right)^{5}n^{10}m^{25}m^{8}n^{9}}{27}$$

Calculate -3 to the power of 5 and get -243.

$$\frac{-243n^{10}m^{25}m^{8}n^{9}}{27}$$

To multiply powers of the same base, add their exponents. Add 25 and 8 to get 33.

$$\frac{-243n^{10}m^{33}n^{9}}{27}$$

To multiply powers of the same base, add their exponents. Add 10 and 9 to get 19.

$$\frac{-243n^{19}m^{33}}{27}$$

Divide -243n^{19}m^{33} by 27 to get -9n^{19}m^{33}.

$$-9n^{19}m^{33}$$

Expand

$$-9n^{19}m^{33}$$

Solution Steps

Cancel out n^{2} in both numerator and denominator.

$$\frac{\left(-3n^{2}m^{5}\right)^{5}}{27}m^{8}n^{9}$$

Express \frac{\left(-3n^{2}m^{5}\right)^{5}}{27}m^{8} as a single fraction.

$$\frac{\left(-3n^{2}m^{5}\right)^{5}m^{8}}{27}n^{9}$$

Express \frac{\left(-3n^{2}m^{5}\right)^{5}m^{8}}{27}n^{9} as a single fraction.

$$\frac{\left(-3n^{2}m^{5}\right)^{5}m^{8}n^{9}}{27}$$

Expand \left(-3n^{2}m^{5}\right)^{5}.

$$\frac{\left(-3\right)^{5}\left(n^{2}\right)^{5}\left(m^{5}\right)^{5}m^{8}n^{9}}{27}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\frac{\left(-3\right)^{5}n^{10}\left(m^{5}\right)^{5}m^{8}n^{9}}{27}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 5 to get 25.

$$\frac{\left(-3\right)^{5}n^{10}m^{25}m^{8}n^{9}}{27}$$

Calculate -3 to the power of 5 and get -243.

$$\frac{-243n^{10}m^{25}m^{8}n^{9}}{27}$$

To multiply powers of the same base, add their exponents. Add 25 and 8 to get 33.

$$\frac{-243n^{10}m^{33}n^{9}}{27}$$

To multiply powers of the same base, add their exponents. Add 10 and 9 to get 19.

$$\frac{-243n^{19}m^{33}}{27}$$

Divide -243n^{19}m^{33} by 27 to get -9n^{19}m^{33}.

$$-9n^{19}m^{33}$$