Solve 3ab(2ab^2)^4

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

Evaluate

$$48a^{5}b^{9}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$3ab\times 2^{4}a^{4}b^{8}$$

Calculate 2 to the power of 4 and get 16.

$$3ab\times 16a^{4}b^{8}$$

Multiply 3 and 16 to get 48.

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

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

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

To multiply powers of the same base, add their exponents. Add 1 and 8 to get 9.

$$48a^{5}b^{9}$$

Expand

$$48a^{5}b^{9}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$3ab\times 2^{4}a^{4}b^{8}$$

Calculate 2 to the power of 4 and get 16.

$$3ab\times 16a^{4}b^{8}$$

Multiply 3 and 16 to get 48.

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

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

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

To multiply powers of the same base, add their exponents. Add 1 and 8 to get 9.

$$48a^{5}b^{9}$$