Solve 2a(3a^2b)^2

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

Evaluate

$$18b^{2}a^{5}$$

Solution Steps

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

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

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

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

Calculate 3 to the power of 2 and get 9.

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

Multiply 2 and 9 to get 18.

$$18aa^{4}b^{2}$$

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

$$18a^{5}b^{2}$$

Expand

$$18b^{2}a^{5}$$

Solution Steps

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

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

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

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

Calculate 3 to the power of 2 and get 9.

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

Multiply 2 and 9 to get 18.

$$18aa^{4}b^{2}$$

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

$$18a^{5}b^{2}$$