Solve (-3a^{3})^{2}*a^{3}+(-4a^2)a^3-(-5a^3)^3

$$( - 3 a ^ { 3 } ) ^ { 2 } \cdot a ^ { 3 } + ( - 4 a ^ { 2 } ) a ^ { 3 } - ( - 5 a ^ { 3 } ) ^ { 3 }$$

Evaluate

$$134a^{9}-4a^{5}$$

Solution Steps

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

$$\left(-3a^{3}\right)^{2}a^{3}-4a^{5}-\left(-5a^{3}\right)^{3}$$

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

$$\left(-3\right)^{2}\left(a^{3}\right)^{2}a^{3}-4a^{5}-\left(-5a^{3}\right)^{3}$$

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

$$\left(-3\right)^{2}a^{6}a^{3}-4a^{5}-\left(-5a^{3}\right)^{3}$$

Calculate -3 to the power of 2 and get 9.

$$9a^{6}a^{3}-4a^{5}-\left(-5a^{3}\right)^{3}$$

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

$$9a^{9}-4a^{5}-\left(-5a^{3}\right)^{3}$$

Expand \left(-5a^{3}\right)^{3}.

$$9a^{9}-4a^{5}-\left(-5\right)^{3}\left(a^{3}\right)^{3}$$

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

$$9a^{9}-4a^{5}-\left(-5\right)^{3}a^{9}$$

Calculate -5 to the power of 3 and get -125.

$$9a^{9}-4a^{5}-\left(-125a^{9}\right)$$

The opposite of -125a^{9} is 125a^{9}.

$$9a^{9}-4a^{5}+125a^{9}$$

Combine 9a^{9} and 125a^{9} to get 134a^{9}.

$$134a^{9}-4a^{5}$$

Expand

$$134a^{9}-4a^{5}$$

Solution Steps

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

$$\left(-3a^{3}\right)^{2}a^{3}-4a^{5}-\left(-5a^{3}\right)^{3}$$

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

$$\left(-3\right)^{2}\left(a^{3}\right)^{2}a^{3}-4a^{5}-\left(-5a^{3}\right)^{3}$$

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

$$\left(-3\right)^{2}a^{6}a^{3}-4a^{5}-\left(-5a^{3}\right)^{3}$$

Calculate -3 to the power of 2 and get 9.

$$9a^{6}a^{3}-4a^{5}-\left(-5a^{3}\right)^{3}$$

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

$$9a^{9}-4a^{5}-\left(-5a^{3}\right)^{3}$$

Expand \left(-5a^{3}\right)^{3}.

$$9a^{9}-4a^{5}-\left(-5\right)^{3}\left(a^{3}\right)^{3}$$

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

$$9a^{9}-4a^{5}-\left(-5\right)^{3}a^{9}$$

Calculate -5 to the power of 3 and get -125.

$$9a^{9}-4a^{5}-\left(-125a^{9}\right)$$

The opposite of -125a^{9} is 125a^{9}.

$$9a^{9}-4a^{5}+125a^{9}$$

Combine 9a^{9} and 125a^{9} to get 134a^{9}.

$$134a^{9}-4a^{5}$$