Solve [(-a)*(-b)^2*a^2b^3c]^2

$$[ ( - a ) \cdot ( - b ) ^ { 2 } \cdot a ^ { 2 } b ^ { 3 } c ] ^ { 2 }$$

Evaluate

$$c^{2}a^{6}b^{10}$$

Solution Steps

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

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

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\left(-a\right)^{2}b^{10}\left(a^{2}\right)^{2}c^{2}$$

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

$$\left(-a\right)^{2}b^{10}a^{4}c^{2}$$

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

$$a^{2}b^{10}a^{4}c^{2}$$

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

$$a^{6}b^{10}c^{2}$$

Expand

$$c^{2}a^{6}b^{10}$$

Solution Steps

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

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

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\left(-a\right)^{2}b^{10}\left(a^{2}\right)^{2}c^{2}$$

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

$$\left(-a\right)^{2}b^{10}a^{4}c^{2}$$

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

$$a^{2}b^{10}a^{4}c^{2}$$

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

$$a^{6}b^{10}c^{2}$$