Solve (-5a^{6})^2+(-3a^3)^3*(-a^3)

$$( - 5 a ^ { 6 } ) ^ { 2 } + ( - 3 a ^ { 3 } ) ^ { 3 } \cdot ( - a ^ { 3 } )$$

Evaluate

$$52a^{12}$$

Solution Steps

Expand \left(-5a^{6}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\left(-5\right)^{2}a^{12}+\left(-3a^{3}\right)^{3}\left(-a^{3}\right)$$

Calculate -5 to the power of 2 and get 25.

$$25a^{12}+\left(-3a^{3}\right)^{3}\left(-a^{3}\right)$$

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

$$25a^{12}+\left(-3\right)^{3}\left(a^{3}\right)^{3}\left(-a^{3}\right)$$

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

$$25a^{12}+\left(-3\right)^{3}a^{9}\left(-a^{3}\right)$$

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

$$25a^{12}-27a^{9}\left(-a^{3}\right)$$

Multiply -27 and -1 to get 27.

$$25a^{12}+27a^{9}a^{3}$$

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

$$25a^{12}+27a^{12}$$

Combine 25a^{12} and 27a^{12} to get 52a^{12}.

$$52a^{12}$$

Expand

$$52a^{12}$$

Solution Steps

Expand \left(-5a^{6}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\left(-5\right)^{2}a^{12}+\left(-3a^{3}\right)^{3}\left(-a^{3}\right)$$

Calculate -5 to the power of 2 and get 25.

$$25a^{12}+\left(-3a^{3}\right)^{3}\left(-a^{3}\right)$$

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

$$25a^{12}+\left(-3\right)^{3}\left(a^{3}\right)^{3}\left(-a^{3}\right)$$

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

$$25a^{12}+\left(-3\right)^{3}a^{9}\left(-a^{3}\right)$$

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

$$25a^{12}-27a^{9}\left(-a^{3}\right)$$

Multiply -27 and -1 to get 27.

$$25a^{12}+27a^{9}a^{3}$$

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

$$25a^{12}+27a^{12}$$

Combine 25a^{12} and 27a^{12} to get 52a^{12}.

$$52a^{12}$$