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

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

Evaluate

$$48b^{5}a^{8}$$

Solution Steps

Expand \left(-4a^{3}b^{2}\right)^{2}.

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

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

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

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

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

Calculate -4 to the power of 2 and get 16.

$$16a^{6}b^{4}\times 3a^{2}b$$

Multiply 16 and 3 to get 48.

$$48a^{6}b^{4}a^{2}b$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$48a^{8}b^{4}b$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$48a^{8}b^{5}$$

Expand

$$48b^{5}a^{8}$$

Solution Steps

Expand \left(-4a^{3}b^{2}\right)^{2}.

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

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

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

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

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

Calculate -4 to the power of 2 and get 16.

$$16a^{6}b^{4}\times 3a^{2}b$$

Multiply 16 and 3 to get 48.

$$48a^{6}b^{4}a^{2}b$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$48a^{8}b^{4}b$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$48a^{8}b^{5}$$