Solve (2a*3b^2)^2*c*(2bc^3)^3

$$(2a \cdot 3b^2)^2 \cdot c \cdot (2bc^3)^3$$

Evaluate

$$288a^{2}b^{7}c^{10}$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\left(6ab^{2}\right)^{2}c\times \left(2bc^{3}\right)^{3}$$

Expand \left(6ab^{2}\right)^{2}.

$$6^{2}a^{2}\left(b^{2}\right)^{2}c\times \left(2bc^{3}\right)^{3}$$

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

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

Calculate 6 to the power of 2 and get 36.

$$36a^{2}b^{4}c\times \left(2bc^{3}\right)^{3}$$

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

$$36a^{2}b^{4}c\times 2^{3}b^{3}\left(c^{3}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$36a^{2}b^{4}c\times 2^{3}b^{3}c^{9}$$

Calculate 2 to the power of 3 and get 8.

$$36a^{2}b^{4}c\times 8b^{3}c^{9}$$

Multiply 36 and 8 to get 288.

$$288a^{2}b^{4}cb^{3}c^{9}$$

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

$$288a^{2}b^{7}cc^{9}$$

To multiply powers of the same base, add their exponents. Add 1 and 9 to get 10.

$$288a^{2}b^{7}c^{10}$$

Expand

$$288a^{2}b^{7}c^{10}$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\left(6ab^{2}\right)^{2}c\times \left(2bc^{3}\right)^{3}$$

Expand \left(6ab^{2}\right)^{2}.

$$6^{2}a^{2}\left(b^{2}\right)^{2}c\times \left(2bc^{3}\right)^{3}$$

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

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

Calculate 6 to the power of 2 and get 36.

$$36a^{2}b^{4}c\times \left(2bc^{3}\right)^{3}$$

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

$$36a^{2}b^{4}c\times 2^{3}b^{3}\left(c^{3}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$36a^{2}b^{4}c\times 2^{3}b^{3}c^{9}$$

Calculate 2 to the power of 3 and get 8.

$$36a^{2}b^{4}c\times 8b^{3}c^{9}$$

Multiply 36 and 8 to get 288.

$$288a^{2}b^{4}cb^{3}c^{9}$$

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

$$288a^{2}b^{7}cc^{9}$$

To multiply powers of the same base, add their exponents. Add 1 and 9 to get 10.

$$288a^{2}b^{7}c^{10}$$