Solve 6a^{3}b^5a^2(1ab^2a)^2

$$6 a ^ { 3 } b ^ { 5 } a ^ { 2 } ( 1 a b ^ { 2 } a ) ^ { 2 }$$

Evaluate

$$6\left(ab\right)^{9}$$

Solution Steps

Multiply a and a to get a^{2}.

$$6a^{3}b^{5}a^{2}\times \left(1a^{2}b^{2}\right)^{2}$$

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

$$6a^{5}b^{5}\times \left(1a^{2}b^{2}\right)^{2}$$

Expand \left(1a^{2}b^{2}\right)^{2}.

$$6a^{5}b^{5}\times 1^{2}\left(a^{2}\right)^{2}\left(b^{2}\right)^{2}$$

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

$$6a^{5}b^{5}\times 1^{2}a^{4}\left(b^{2}\right)^{2}$$

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

$$6a^{5}b^{5}\times 1^{2}a^{4}b^{4}$$

Calculate 1 to the power of 2 and get 1.

$$6a^{5}b^{5}\times 1a^{4}b^{4}$$

Multiply 6 and 1 to get 6.

$$6a^{5}b^{5}a^{4}b^{4}$$

To multiply powers of the same base, add their exponents. Add 5 and 4 to get 9.

$$6a^{9}b^{5}b^{4}$$

To multiply powers of the same base, add their exponents. Add 5 and 4 to get 9.

$$6a^{9}b^{9}$$

Expand

$$6\left(ab\right)^{9}$$

Solution Steps

Multiply a and a to get a^{2}.

$$6a^{3}b^{5}a^{2}\times \left(1a^{2}b^{2}\right)^{2}$$

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

$$6a^{5}b^{5}\times \left(1a^{2}b^{2}\right)^{2}$$

Expand \left(1a^{2}b^{2}\right)^{2}.

$$6a^{5}b^{5}\times 1^{2}\left(a^{2}\right)^{2}\left(b^{2}\right)^{2}$$

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

$$6a^{5}b^{5}\times 1^{2}a^{4}\left(b^{2}\right)^{2}$$

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

$$6a^{5}b^{5}\times 1^{2}a^{4}b^{4}$$

Calculate 1 to the power of 2 and get 1.

$$6a^{5}b^{5}\times 1a^{4}b^{4}$$

Multiply 6 and 1 to get 6.

$$6a^{5}b^{5}a^{4}b^{4}$$

To multiply powers of the same base, add their exponents. Add 5 and 4 to get 9.

$$6a^{9}b^{5}b^{4}$$

To multiply powers of the same base, add their exponents. Add 5 and 4 to get 9.

$$6a^{9}b^{9}$$