Solve (-a^{2}b^3c^4)(-xa^2b)^2

$$( - a ^ { 2 } b ^ { 3 } c ^ { 4 } ) ( - x a ^ { 2 } b ) ^ { 2 }$$

Evaluate

$$-x^{2}c^{4}b^{5}a^{6}$$

Solution Steps

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

$$\left(-a^{2}\right)b^{3}c^{4}\left(-x\right)^{2}\left(a^{2}\right)^{2}b^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\left(-a^{2}\right)b^{3}c^{4}\left(-x\right)^{2}a^{4}b^{2}$$

Calculate -x to the power of 2 and get x^{2}.

$$\left(-a^{2}\right)b^{3}c^{4}x^{2}a^{4}b^{2}$$

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

$$\left(-a^{2}\right)b^{5}c^{4}x^{2}a^{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$-a^{6}b^{5}c^{4}x^{2}$$

Expand

$$-x^{2}c^{4}b^{5}a^{6}$$

Solution Steps

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

$$\left(-a^{2}\right)b^{3}c^{4}\left(-x\right)^{2}\left(a^{2}\right)^{2}b^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\left(-a^{2}\right)b^{3}c^{4}\left(-x\right)^{2}a^{4}b^{2}$$

Calculate -x to the power of 2 and get x^{2}.

$$\left(-a^{2}\right)b^{3}c^{4}x^{2}a^{4}b^{2}$$

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

$$\left(-a^{2}\right)b^{5}c^{4}x^{2}a^{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$-a^{6}b^{5}c^{4}x^{2}$$