Solve (a2^2b)^3(2a^2b)^2=

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

Evaluate

$$256b^{5}a^{7}$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

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

Expand \left(a\times 4b\right)^{3}.

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

Calculate 4 to the power of 3 and get 64.

$$a^{3}\times 64b^{3}\times \left(2a^{2}b\right)^{2}$$

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

$$a^{3}\times 64b^{3}\times 2^{2}\left(a^{2}\right)^{2}b^{2}$$

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

$$a^{3}\times 64b^{3}\times 2^{2}a^{4}b^{2}$$

Calculate 2 to the power of 2 and get 4.

$$a^{3}\times 64b^{3}\times 4a^{4}b^{2}$$

Multiply 64 and 4 to get 256.

$$a^{3}\times 256b^{3}a^{4}b^{2}$$

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

$$a^{7}\times 256b^{3}b^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$a^{7}\times 256b^{5}$$

Expand

$$256b^{5}a^{7}$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

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

Expand \left(a\times 4b\right)^{3}.

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

Calculate 4 to the power of 3 and get 64.

$$a^{3}\times 64b^{3}\times \left(2a^{2}b\right)^{2}$$

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

$$a^{3}\times 64b^{3}\times 2^{2}\left(a^{2}\right)^{2}b^{2}$$

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

$$a^{3}\times 64b^{3}\times 2^{2}a^{4}b^{2}$$

Calculate 2 to the power of 2 and get 4.

$$a^{3}\times 64b^{3}\times 4a^{4}b^{2}$$

Multiply 64 and 4 to get 256.

$$a^{3}\times 256b^{3}a^{4}b^{2}$$

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

$$a^{7}\times 256b^{3}b^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$a^{7}\times 256b^{5}$$