Solve (-3a^2x)^3*(-ax)^5(3a)^3

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

Evaluate

$$729x^{8}a^{14}$$

Solution Steps

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

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

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

$$\left(-3\right)^{3}a^{6}x^{3}\left(\left(-a\right)x\right)^{5}\times \left(3a\right)^{3}$$

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

$$-27a^{6}x^{3}\left(\left(-a\right)x\right)^{5}\times \left(3a\right)^{3}$$

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

$$-27a^{6}x^{3}\left(-a\right)^{5}x^{5}\times \left(3a\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$-27a^{6}x^{8}\left(-a\right)^{5}\times \left(3a\right)^{3}$$

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

$$-27a^{6}x^{8}\left(-a\right)^{5}\times 3^{3}a^{3}$$

Calculate 3 to the power of 3 and get 27.

$$-27a^{6}x^{8}\left(-a\right)^{5}\times 27a^{3}$$

Multiply -27 and 27 to get -729.

$$-729a^{6}x^{8}\left(-a\right)^{5}a^{3}$$

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

$$-729a^{9}x^{8}\left(-a\right)^{5}$$

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

$$-729a^{9}x^{8}\left(-1\right)^{5}a^{5}$$

Calculate -1 to the power of 5 and get -1.

$$-729a^{9}x^{8}\left(-1\right)a^{5}$$

Multiply -729 and -1 to get 729.

$$729a^{9}x^{8}a^{5}$$

To multiply powers of the same base, add their exponents. Add 9 and 5 to get 14.

$$729a^{14}x^{8}$$

Expand

$$729x^{8}a^{14}$$

Solution Steps

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

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

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

$$\left(-3\right)^{3}a^{6}x^{3}\left(\left(-a\right)x\right)^{5}\times \left(3a\right)^{3}$$

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

$$-27a^{6}x^{3}\left(\left(-a\right)x\right)^{5}\times \left(3a\right)^{3}$$

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

$$-27a^{6}x^{3}\left(-a\right)^{5}x^{5}\times \left(3a\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$-27a^{6}x^{8}\left(-a\right)^{5}\times \left(3a\right)^{3}$$

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

$$-27a^{6}x^{8}\left(-a\right)^{5}\times 3^{3}a^{3}$$

Calculate 3 to the power of 3 and get 27.

$$-27a^{6}x^{8}\left(-a\right)^{5}\times 27a^{3}$$

Multiply -27 and 27 to get -729.

$$-729a^{6}x^{8}\left(-a\right)^{5}a^{3}$$

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

$$-729a^{9}x^{8}\left(-a\right)^{5}$$

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

$$-729a^{9}x^{8}\left(-1\right)^{5}a^{5}$$

Calculate -1 to the power of 5 and get -1.

$$-729a^{9}x^{8}\left(-1\right)a^{5}$$

Multiply -729 and -1 to get 729.

$$729a^{9}x^{8}a^{5}$$

To multiply powers of the same base, add their exponents. Add 9 and 5 to get 14.

$$729a^{14}x^{8}$$