Solve (4a^7b)^2*(3ab^6)^2

$$( 4 a ^ { 7 } b ) ^ { 2 } \times ( 3 a b ^ { 6 } ) ^ { 2 }$$

Evaluate

$$144b^{14}a^{16}$$

Solution Steps

Expand \left(4a^{7}b\right)^{2}.

$$4^{2}\left(a^{7}\right)^{2}b^{2}\times \left(3ab^{6}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$4^{2}a^{14}b^{2}\times \left(3ab^{6}\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$16a^{14}b^{2}\times \left(3ab^{6}\right)^{2}$$

Expand \left(3ab^{6}\right)^{2}.

$$16a^{14}b^{2}\times 3^{2}a^{2}\left(b^{6}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$16a^{14}b^{2}\times 3^{2}a^{2}b^{12}$$

Calculate 3 to the power of 2 and get 9.

$$16a^{14}b^{2}\times 9a^{2}b^{12}$$

Multiply 16 and 9 to get 144.

$$144a^{14}b^{2}a^{2}b^{12}$$

To multiply powers of the same base, add their exponents. Add 14 and 2 to get 16.

$$144a^{16}b^{2}b^{12}$$

To multiply powers of the same base, add their exponents. Add 2 and 12 to get 14.

$$144a^{16}b^{14}$$

Expand

$$144b^{14}a^{16}$$

Solution Steps

Expand \left(4a^{7}b\right)^{2}.

$$4^{2}\left(a^{7}\right)^{2}b^{2}\times \left(3ab^{6}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$4^{2}a^{14}b^{2}\times \left(3ab^{6}\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$16a^{14}b^{2}\times \left(3ab^{6}\right)^{2}$$

Expand \left(3ab^{6}\right)^{2}.

$$16a^{14}b^{2}\times 3^{2}a^{2}\left(b^{6}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$16a^{14}b^{2}\times 3^{2}a^{2}b^{12}$$

Calculate 3 to the power of 2 and get 9.

$$16a^{14}b^{2}\times 9a^{2}b^{12}$$

Multiply 16 and 9 to get 144.

$$144a^{14}b^{2}a^{2}b^{12}$$

To multiply powers of the same base, add their exponents. Add 14 and 2 to get 16.

$$144a^{16}b^{2}b^{12}$$

To multiply powers of the same base, add their exponents. Add 2 and 12 to get 14.

$$144a^{16}b^{14}$$