Solve (2m^-6n^4)^9*-m^2

$$( 2 m ^ { - 6 } n ^ { 4 } ) ^ { 9 } \cdot - m ^ { 2 }$$

Evaluate

$$-\frac{512n^{36}}{m^{52}}$$

Solution Steps

Expand \left(2m^{-6}n^{4}\right)^{9}.

$$2^{9}\left(m^{-6}\right)^{9}\left(n^{4}\right)^{9}\left(-m^{2}\right)$$

To raise a power to another power, multiply the exponents. Multiply -6 and 9 to get -54.

$$2^{9}m^{-54}\left(n^{4}\right)^{9}\left(-m^{2}\right)$$

To raise a power to another power, multiply the exponents. Multiply 4 and 9 to get 36.

$$2^{9}m^{-54}n^{36}\left(-m^{2}\right)$$

Calculate 2 to the power of 9 and get 512.

$$512m^{-54}n^{36}\left(-m^{2}\right)$$

Multiply 512 and -1 to get -512.

$$-512m^{-54}n^{36}m^{2}$$

To multiply powers of the same base, add their exponents. Add -54 and 2 to get -52.

$$-512m^{-52}n^{36}$$

Expand

$$-\frac{512n^{36}}{m^{52}}$$

Solution Steps

Expand \left(2m^{-6}n^{4}\right)^{9}.

$$2^{9}\left(m^{-6}\right)^{9}\left(n^{4}\right)^{9}\left(-m^{2}\right)$$

To raise a power to another power, multiply the exponents. Multiply -6 and 9 to get -54.

$$2^{9}m^{-54}\left(n^{4}\right)^{9}\left(-m^{2}\right)$$

To raise a power to another power, multiply the exponents. Multiply 4 and 9 to get 36.

$$2^{9}m^{-54}n^{36}\left(-m^{2}\right)$$

Calculate 2 to the power of 9 and get 512.

$$512m^{-54}n^{36}\left(-m^{2}\right)$$

Multiply 512 and -1 to get -512.

$$-512m^{-54}n^{36}m^{2}$$

To multiply powers of the same base, add their exponents. Add -54 and 2 to get -52.

$$-512m^{-52}n^{36}$$