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

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

Evaluate

$$-48a^{5}b^{7}$$

Solution Steps

Expand \left(4ab^{2}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$-3a^{3}b^{3}\times 4^{2}a^{2}b^{4}$$

Calculate 4 to the power of 2 and get 16.

$$-3a^{3}b^{3}\times 16a^{2}b^{4}$$

Multiply -3 and 16 to get -48.

$$-48a^{3}b^{3}a^{2}b^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$-48a^{5}b^{3}b^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$-48a^{5}b^{7}$$

Expand

$$-48a^{5}b^{7}$$

Solution Steps

Expand \left(4ab^{2}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$-3a^{3}b^{3}\times 4^{2}a^{2}b^{4}$$

Calculate 4 to the power of 2 and get 16.

$$-3a^{3}b^{3}\times 16a^{2}b^{4}$$

Multiply -3 and 16 to get -48.

$$-48a^{3}b^{3}a^{2}b^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$-48a^{5}b^{3}b^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$-48a^{5}b^{7}$$