Solve (2a^2b)^3(-3ab^8)^2

$$( 2 a ^ { 2 } b ) ^ { 3 } ( - 3 a b ^ { 8 } ) ^ { 2 }$$

Evaluate

$$72a^{8}b^{19}$$

Solution Steps

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

$$2^{3}\left(a^{2}\right)^{3}b^{3}\left(-3ab^{8}\right)^{2}$$

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

$$2^{3}a^{6}b^{3}\left(-3ab^{8}\right)^{2}$$

Calculate 2 to the power of 3 and get 8.

$$8a^{6}b^{3}\left(-3ab^{8}\right)^{2}$$

Expand \left(-3ab^{8}\right)^{2}.

$$8a^{6}b^{3}\left(-3\right)^{2}a^{2}\left(b^{8}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 2 to get 16.

$$8a^{6}b^{3}\left(-3\right)^{2}a^{2}b^{16}$$

Calculate -3 to the power of 2 and get 9.

$$8a^{6}b^{3}\times 9a^{2}b^{16}$$

Multiply 8 and 9 to get 72.

$$72a^{6}b^{3}a^{2}b^{16}$$

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

$$72a^{8}b^{3}b^{16}$$

To multiply powers of the same base, add their exponents. Add 3 and 16 to get 19.

$$72a^{8}b^{19}$$

Expand

$$72a^{8}b^{19}$$

Solution Steps

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

$$2^{3}\left(a^{2}\right)^{3}b^{3}\left(-3ab^{8}\right)^{2}$$

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

$$2^{3}a^{6}b^{3}\left(-3ab^{8}\right)^{2}$$

Calculate 2 to the power of 3 and get 8.

$$8a^{6}b^{3}\left(-3ab^{8}\right)^{2}$$

Expand \left(-3ab^{8}\right)^{2}.

$$8a^{6}b^{3}\left(-3\right)^{2}a^{2}\left(b^{8}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 2 to get 16.

$$8a^{6}b^{3}\left(-3\right)^{2}a^{2}b^{16}$$

Calculate -3 to the power of 2 and get 9.

$$8a^{6}b^{3}\times 9a^{2}b^{16}$$

Multiply 8 and 9 to get 72.

$$72a^{6}b^{3}a^{2}b^{16}$$

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

$$72a^{8}b^{3}b^{16}$$

To multiply powers of the same base, add their exponents. Add 3 and 16 to get 19.

$$72a^{8}b^{19}$$