Solve (7)[(-m^{2})^{3}]^3+[(m^3)^3]^2

$$( 7 ) [ ( - m ^ { 2 } ) ^ { 3 } ] ^ { 3 } + [ ( m ^ { 3 } ) ^ { 3 } ] ^ { 2 }$$

Evaluate

$$-6m^{18}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$7\left(-m^{2}\right)^{9}+\left(\left(m^{3}\right)^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$7\left(-m^{2}\right)^{9}+\left(m^{9}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 2 to get 18.

$$7\left(-m^{2}\right)^{9}+m^{18}$$

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

$$7\left(-1\right)^{9}\left(m^{2}\right)^{9}+m^{18}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 9 to get 18.

$$7\left(-1\right)^{9}m^{18}+m^{18}$$

Calculate -1 to the power of 9 and get -1.

$$7\left(-1\right)m^{18}+m^{18}$$

Multiply 7 and -1 to get -7.

$$-7m^{18}+m^{18}$$

Combine -7m^{18} and m^{18} to get -6m^{18}.

$$-6m^{18}$$

Expand

$$-6m^{18}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$7\left(-m^{2}\right)^{9}+\left(\left(m^{3}\right)^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$7\left(-m^{2}\right)^{9}+\left(m^{9}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 2 to get 18.

$$7\left(-m^{2}\right)^{9}+m^{18}$$

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

$$7\left(-1\right)^{9}\left(m^{2}\right)^{9}+m^{18}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 9 to get 18.

$$7\left(-1\right)^{9}m^{18}+m^{18}$$

Calculate -1 to the power of 9 and get -1.

$$7\left(-1\right)m^{18}+m^{18}$$

Multiply 7 and -1 to get -7.

$$-7m^{18}+m^{18}$$

Combine -7m^{18} and m^{18} to get -6m^{18}.

$$-6m^{18}$$