Solve (-3a^{2})^{3}*a^{3}+(-4a)^2*a^7-(5a^3)^3=

$$( - 3 a ^ { 2 } ) ^ { 3 } \cdot a ^ { 3 } + ( - 4 a ) ^ { 2 } \cdot a ^ { 7 } - ( 5 a ^ { 3 } ) ^ { 3 } =$$

Evaluate

$$-136a^{9}$$

Solution Steps

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

$$\left(-3\right)^{3}\left(a^{2}\right)^{3}a^{3}+\left(-4a\right)^{2}a^{7}-\left(5a^{3}\right)^{3}$$

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

$$\left(-3\right)^{3}a^{6}a^{3}+\left(-4a\right)^{2}a^{7}-\left(5a^{3}\right)^{3}$$

Calculate -3 to the power of 3 and get -27.

$$-27a^{6}a^{3}+\left(-4a\right)^{2}a^{7}-\left(5a^{3}\right)^{3}$$

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

$$-27a^{9}+\left(-4a\right)^{2}a^{7}-\left(5a^{3}\right)^{3}$$

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

$$-27a^{9}+\left(-4\right)^{2}a^{2}a^{7}-\left(5a^{3}\right)^{3}$$

Calculate -4 to the power of 2 and get 16.

$$-27a^{9}+16a^{2}a^{7}-\left(5a^{3}\right)^{3}$$

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

$$-27a^{9}+16a^{9}-\left(5a^{3}\right)^{3}$$

Combine -27a^{9} and 16a^{9} to get -11a^{9}.

$$-11a^{9}-\left(5a^{3}\right)^{3}$$

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

$$-11a^{9}-5^{3}\left(a^{3}\right)^{3}$$

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

$$-11a^{9}-5^{3}a^{9}$$

Calculate 5 to the power of 3 and get 125.

$$-11a^{9}-125a^{9}$$

Combine -11a^{9} and -125a^{9} to get -136a^{9}.

$$-136a^{9}$$

Expand

$$-136a^{9}$$

Solution Steps

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

$$\left(-3\right)^{3}\left(a^{2}\right)^{3}a^{3}+\left(-4a\right)^{2}a^{7}-\left(5a^{3}\right)^{3}$$

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

$$\left(-3\right)^{3}a^{6}a^{3}+\left(-4a\right)^{2}a^{7}-\left(5a^{3}\right)^{3}$$

Calculate -3 to the power of 3 and get -27.

$$-27a^{6}a^{3}+\left(-4a\right)^{2}a^{7}-\left(5a^{3}\right)^{3}$$

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

$$-27a^{9}+\left(-4a\right)^{2}a^{7}-\left(5a^{3}\right)^{3}$$

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

$$-27a^{9}+\left(-4\right)^{2}a^{2}a^{7}-\left(5a^{3}\right)^{3}$$

Calculate -4 to the power of 2 and get 16.

$$-27a^{9}+16a^{2}a^{7}-\left(5a^{3}\right)^{3}$$

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

$$-27a^{9}+16a^{9}-\left(5a^{3}\right)^{3}$$

Combine -27a^{9} and 16a^{9} to get -11a^{9}.

$$-11a^{9}-\left(5a^{3}\right)^{3}$$

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

$$-11a^{9}-5^{3}\left(a^{3}\right)^{3}$$

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

$$-11a^{9}-5^{3}a^{9}$$

Calculate 5 to the power of 3 and get 125.

$$-11a^{9}-125a^{9}$$

Combine -11a^{9} and -125a^{9} to get -136a^{9}.

$$-136a^{9}$$