Solve (3a^{3})^{2}*a^{3}+(-4a^2)*a^7-(2a^3)^3

$$( 3 a ^ { 3 } ) ^ { 2 } \cdot a ^ { 3 } + ( - 4 a ^ { 2 } ) \cdot a ^ { 7 } - ( 2 a ^ { 3 } ) ^ { 3 }$$

Evaluate

$$-3a^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 7 to get 9.

$$\left(3a^{3}\right)^{2}a^{3}-4a^{9}-\left(2a^{3}\right)^{3}$$

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

$$3^{2}\left(a^{3}\right)^{2}a^{3}-4a^{9}-\left(2a^{3}\right)^{3}$$

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

$$3^{2}a^{6}a^{3}-4a^{9}-\left(2a^{3}\right)^{3}$$

Calculate 3 to the power of 2 and get 9.

$$9a^{6}a^{3}-4a^{9}-\left(2a^{3}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$9a^{9}-4a^{9}-\left(2a^{3}\right)^{3}$$

Combine 9a^{9} and -4a^{9} to get 5a^{9}.

$$5a^{9}-\left(2a^{3}\right)^{3}$$

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

$$5a^{9}-2^{3}\left(a^{3}\right)^{3}$$

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

$$5a^{9}-2^{3}a^{9}$$

Calculate 2 to the power of 3 and get 8.

$$5a^{9}-8a^{9}$$

Combine 5a^{9} and -8a^{9} to get -3a^{9}.

$$-3a^{9}$$

Expand

$$-3a^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 7 to get 9.

$$\left(3a^{3}\right)^{2}a^{3}-4a^{9}-\left(2a^{3}\right)^{3}$$

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

$$3^{2}\left(a^{3}\right)^{2}a^{3}-4a^{9}-\left(2a^{3}\right)^{3}$$

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

$$3^{2}a^{6}a^{3}-4a^{9}-\left(2a^{3}\right)^{3}$$

Calculate 3 to the power of 2 and get 9.

$$9a^{6}a^{3}-4a^{9}-\left(2a^{3}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$9a^{9}-4a^{9}-\left(2a^{3}\right)^{3}$$

Combine 9a^{9} and -4a^{9} to get 5a^{9}.

$$5a^{9}-\left(2a^{3}\right)^{3}$$

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

$$5a^{9}-2^{3}\left(a^{3}\right)^{3}$$

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

$$5a^{9}-2^{3}a^{9}$$

Calculate 2 to the power of 3 and get 8.

$$5a^{9}-8a^{9}$$

Combine 5a^{9} and -8a^{9} to get -3a^{9}.

$$-3a^{9}$$