Solve (-m^{2}n^{3})^6div(-m^2n^3)^2

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

Evaluate

$$m^{8}n^{12}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 6 to get 4.

$$\left(\left(-m^{2}\right)n^{3}\right)^{4}$$

Expand \left(\left(-m^{2}\right)n^{3}\right)^{4}.

$$\left(-m^{2}\right)^{4}\left(n^{3}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\left(-m^{2}\right)^{4}n^{12}$$

Expand \left(-m^{2}\right)^{4}.

$$\left(-1\right)^{4}\left(m^{2}\right)^{4}n^{12}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\left(-1\right)^{4}m^{8}n^{12}$$

Calculate -1 to the power of 4 and get 1.

$$1m^{8}n^{12}$$

For any term t, t\times 1=t and 1t=t.

$$m^{8}n^{12}$$

Expand

$$m^{8}n^{12}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 6 to get 4.

$$\left(\left(-m^{2}\right)n^{3}\right)^{4}$$

Expand \left(\left(-m^{2}\right)n^{3}\right)^{4}.

$$\left(-m^{2}\right)^{4}\left(n^{3}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\left(-m^{2}\right)^{4}n^{12}$$

Expand \left(-m^{2}\right)^{4}.

$$\left(-1\right)^{4}\left(m^{2}\right)^{4}n^{12}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\left(-1\right)^{4}m^{8}n^{12}$$

Calculate -1 to the power of 4 and get 1.

$$1m^{8}n^{12}$$

For any term t, t\times 1=t and 1t=t.

$$m^{8}n^{12}$$