Solve (3a^3b^3)^3*3a^3

$$( 3 a ^ { 3 } b ^ { 3 } ) ^ { 3 } \times 3 a ^ { 3 }$$

Evaluate

$$81b^{9}a^{12}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$3^{3}a^{9}\left(b^{3}\right)^{3}\times 3a^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$3^{3}a^{9}b^{9}\times 3a^{3}$$

Calculate 3 to the power of 3 and get 27.

$$27a^{9}b^{9}\times 3a^{3}$$

Multiply 27 and 3 to get 81.

$$81a^{9}b^{9}a^{3}$$

To multiply powers of the same base, add their exponents. Add 9 and 3 to get 12.

$$81a^{12}b^{9}$$

Expand

$$81b^{9}a^{12}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$3^{3}a^{9}\left(b^{3}\right)^{3}\times 3a^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$3^{3}a^{9}b^{9}\times 3a^{3}$$

Calculate 3 to the power of 3 and get 27.

$$27a^{9}b^{9}\times 3a^{3}$$

Multiply 27 and 3 to get 81.

$$81a^{9}b^{9}a^{3}$$

To multiply powers of the same base, add their exponents. Add 9 and 3 to get 12.

$$81a^{12}b^{9}$$