Solve (2a^{3}b^2)^2*a^7b^2

$$( 2 a ^ { 3 } b ^ { 2 } ) ^ { 2 } \cdot a ^ { 7 } b ^ { 2 }$$

Evaluate

$$4b^{6}a^{13}$$

Solution Steps

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

$$2^{2}\left(a^{3}\right)^{2}\left(b^{2}\right)^{2}a^{7}b^{2}$$

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

$$2^{2}a^{6}\left(b^{2}\right)^{2}a^{7}b^{2}$$

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

$$2^{2}a^{6}b^{4}a^{7}b^{2}$$

Calculate 2 to the power of 2 and get 4.

$$4a^{6}b^{4}a^{7}b^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 7 to get 13.

$$4a^{13}b^{4}b^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$4a^{13}b^{6}$$

Expand

$$4b^{6}a^{13}$$

Solution Steps

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

$$2^{2}\left(a^{3}\right)^{2}\left(b^{2}\right)^{2}a^{7}b^{2}$$

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

$$2^{2}a^{6}\left(b^{2}\right)^{2}a^{7}b^{2}$$

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

$$2^{2}a^{6}b^{4}a^{7}b^{2}$$

Calculate 2 to the power of 2 and get 4.

$$4a^{6}b^{4}a^{7}b^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 7 to get 13.

$$4a^{13}b^{4}b^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$4a^{13}b^{6}$$