Solve (3*a^{2})^{3}-3*(2*b^{2})^{4}+a^3*2*a^3+(3*b*b^3)^2

$$( 3 \cdot a ^ { 2 } ) ^ { 3 } - 3 \cdot ( 2 \cdot b ^ { 2 } ) ^ { 4 } + a ^ { 3 } \cdot 2 \cdot a ^ { 3 } + ( 3 \cdot b \cdot b ^ { 3 } ) ^ { 2 }$$

Evaluate

$$29a^{6}-39b^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\left(3a^{2}\right)^{3}-3\times \left(2b^{2}\right)^{4}+a^{6}\times 2+\left(3bb^{3}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

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

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

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

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

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

Calculate 3 to the power of 3 and get 27.

$$27a^{6}-3\times \left(2b^{2}\right)^{4}+a^{6}\times 2+\left(3b^{4}\right)^{2}$$

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

$$27a^{6}-3\times 2^{4}\left(b^{2}\right)^{4}+a^{6}\times 2+\left(3b^{4}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$27a^{6}-3\times 2^{4}b^{8}+a^{6}\times 2+\left(3b^{4}\right)^{2}$$

Calculate 2 to the power of 4 and get 16.

$$27a^{6}-3\times 16b^{8}+a^{6}\times 2+\left(3b^{4}\right)^{2}$$

Multiply 3 and 16 to get 48.

$$27a^{6}-48b^{8}+a^{6}\times 2+\left(3b^{4}\right)^{2}$$

Combine 27a^{6} and a^{6}\times 2 to get 29a^{6}.

$$29a^{6}-48b^{8}+\left(3b^{4}\right)^{2}$$

Expand \left(3b^{4}\right)^{2}.

$$29a^{6}-48b^{8}+3^{2}\left(b^{4}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$29a^{6}-48b^{8}+3^{2}b^{8}$$

Calculate 3 to the power of 2 and get 9.

$$29a^{6}-48b^{8}+9b^{8}$$

Combine -48b^{8} and 9b^{8} to get -39b^{8}.

$$29a^{6}-39b^{8}$$

Expand

$$29a^{6}-39b^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\left(3a^{2}\right)^{3}-3\times \left(2b^{2}\right)^{4}+a^{6}\times 2+\left(3bb^{3}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

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

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

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

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

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

Calculate 3 to the power of 3 and get 27.

$$27a^{6}-3\times \left(2b^{2}\right)^{4}+a^{6}\times 2+\left(3b^{4}\right)^{2}$$

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

$$27a^{6}-3\times 2^{4}\left(b^{2}\right)^{4}+a^{6}\times 2+\left(3b^{4}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$27a^{6}-3\times 2^{4}b^{8}+a^{6}\times 2+\left(3b^{4}\right)^{2}$$

Calculate 2 to the power of 4 and get 16.

$$27a^{6}-3\times 16b^{8}+a^{6}\times 2+\left(3b^{4}\right)^{2}$$

Multiply 3 and 16 to get 48.

$$27a^{6}-48b^{8}+a^{6}\times 2+\left(3b^{4}\right)^{2}$$

Combine 27a^{6} and a^{6}\times 2 to get 29a^{6}.

$$29a^{6}-48b^{8}+\left(3b^{4}\right)^{2}$$

Expand \left(3b^{4}\right)^{2}.

$$29a^{6}-48b^{8}+3^{2}\left(b^{4}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$29a^{6}-48b^{8}+3^{2}b^{8}$$

Calculate 3 to the power of 2 and get 9.

$$29a^{6}-48b^{8}+9b^{8}$$

Combine -48b^{8} and 9b^{8} to get -39b^{8}.

$$29a^{6}-39b^{8}$$