Solve (-4g^3)(-g^6b^5)^2

$$( - 4 g ^ { 3 } ) ( - g ^ { 6 } b ^ { 5 } ) ^ { 2 }$$

Evaluate

$$-4b^{10}g^{15}$$

Solution Steps

Expand \left(\left(-g^{6}\right)b^{5}\right)^{2}.

$$-4g^{3}\left(-g^{6}\right)^{2}\left(b^{5}\right)^{2}$$

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

$$-4g^{3}\left(-g^{6}\right)^{2}b^{10}$$

Calculate -g^{6} to the power of 2 and get \left(g^{6}\right)^{2}.

$$-4g^{3}\left(g^{6}\right)^{2}b^{10}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$-4g^{3}g^{12}b^{10}$$

To multiply powers of the same base, add their exponents. Add 3 and 12 to get 15.

$$-4g^{15}b^{10}$$

Expand

$$-4b^{10}g^{15}$$

Solution Steps

Expand \left(\left(-g^{6}\right)b^{5}\right)^{2}.

$$-4g^{3}\left(-g^{6}\right)^{2}\left(b^{5}\right)^{2}$$

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

$$-4g^{3}\left(-g^{6}\right)^{2}b^{10}$$

Calculate -g^{6} to the power of 2 and get \left(g^{6}\right)^{2}.

$$-4g^{3}\left(g^{6}\right)^{2}b^{10}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$-4g^{3}g^{12}b^{10}$$

To multiply powers of the same base, add their exponents. Add 3 and 12 to get 15.

$$-4g^{15}b^{10}$$