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

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

Evaluate

$$36\left(ab\right)^{6}$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

Calculate 3 to the power of 2 and get 9.

$$4a^{2}b^{4}\times 9a^{4}b^{2}$$

Multiply 4 and 9 to get 36.

$$36a^{2}b^{4}a^{4}b^{2}$$

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

$$36a^{6}b^{4}b^{2}$$

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

$$36a^{6}b^{6}$$

Expand

$$36\left(ab\right)^{6}$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

Calculate 3 to the power of 2 and get 9.

$$4a^{2}b^{4}\times 9a^{4}b^{2}$$

Multiply 4 and 9 to get 36.

$$36a^{2}b^{4}a^{4}b^{2}$$

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

$$36a^{6}b^{4}b^{2}$$

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

$$36a^{6}b^{6}$$