Solve (m^{3})^{4}(2x^{3})^{7}(m^3)^4(x^3)^7

$$( m ^ { 3 } ) ^ { 4 } ( 2 x ^ { 3 } ) ^ { 7 } ( m ^ { 3 } ) ^ { 4 } ( x ^ { 3 } ) ^ { 7 }$$

Evaluate

$$128m^{24}x^{42}$$

Solution Steps

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

$$m^{12}\times \left(2x^{3}\right)^{7}\left(m^{3}\right)^{4}\left(x^{3}\right)^{7}$$

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

$$m^{12}\times \left(2x^{3}\right)^{7}m^{12}\left(x^{3}\right)^{7}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 7 to get 21.

$$m^{12}\times \left(2x^{3}\right)^{7}m^{12}x^{21}$$

To multiply powers of the same base, add their exponents. Add 12 and 12 to get 24.

$$m^{24}\times \left(2x^{3}\right)^{7}x^{21}$$

Expand \left(2x^{3}\right)^{7}.

$$m^{24}\times 2^{7}\left(x^{3}\right)^{7}x^{21}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 7 to get 21.

$$m^{24}\times 2^{7}x^{21}x^{21}$$

Calculate 2 to the power of 7 and get 128.

$$m^{24}\times 128x^{21}x^{21}$$

To multiply powers of the same base, add their exponents. Add 21 and 21 to get 42.

$$m^{24}\times 128x^{42}$$

Expand

$$128m^{24}x^{42}$$

Solution Steps

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

$$m^{12}\times \left(2x^{3}\right)^{7}\left(m^{3}\right)^{4}\left(x^{3}\right)^{7}$$

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

$$m^{12}\times \left(2x^{3}\right)^{7}m^{12}\left(x^{3}\right)^{7}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 7 to get 21.

$$m^{12}\times \left(2x^{3}\right)^{7}m^{12}x^{21}$$

To multiply powers of the same base, add their exponents. Add 12 and 12 to get 24.

$$m^{24}\times \left(2x^{3}\right)^{7}x^{21}$$

Expand \left(2x^{3}\right)^{7}.

$$m^{24}\times 2^{7}\left(x^{3}\right)^{7}x^{21}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 7 to get 21.

$$m^{24}\times 2^{7}x^{21}x^{21}$$

Calculate 2 to the power of 7 and get 128.

$$m^{24}\times 128x^{21}x^{21}$$

To multiply powers of the same base, add their exponents. Add 21 and 21 to get 42.

$$m^{24}\times 128x^{42}$$