Solve (5ab^3)^2(-3a^4)

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

Evaluate

$$-75\left(ab\right)^{6}$$

Solution Steps

Expand \left(5ab^{3}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

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

Calculate 5 to the power of 2 and get 25.

$$25a^{2}b^{6}\left(-3\right)a^{4}$$

Multiply 25 and -3 to get -75.

$$-75a^{2}b^{6}a^{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$-75a^{6}b^{6}$$

Expand

$$-75\left(ab\right)^{6}$$

Solution Steps

Expand \left(5ab^{3}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

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

Calculate 5 to the power of 2 and get 25.

$$25a^{2}b^{6}\left(-3\right)a^{4}$$

Multiply 25 and -3 to get -75.

$$-75a^{2}b^{6}a^{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$-75a^{6}b^{6}$$