Solve (5/4a^{3}bc^{2}-a^{3}bc^2-1/2a^3bc^2)^2

$$( \frac { 5 } { 4 } a ^ { 3 } b c ^ { 2 } - a ^ { 3 } b c ^ { 2 } - \frac { 1 } { 2 } a ^ { 3 } b c ^ { 2 } ) ^ { 2 }$$

Evaluate

$$\frac{b^{2}c^{4}a^{6}}{16}$$

Solution Steps

Combine \frac{5}{4}a^{3}bc^{2} and -a^{3}bc^{2} to get \frac{1}{4}a^{3}bc^{2}.

$$\left(\frac{1}{4}a^{3}bc^{2}-\frac{1}{2}a^{3}bc^{2}\right)^{2}$$

Combine \frac{1}{4}a^{3}bc^{2} and -\frac{1}{2}a^{3}bc^{2} to get -\frac{1}{4}a^{3}bc^{2}.

$$\left(-\frac{1}{4}a^{3}bc^{2}\right)^{2}$$

Expand \left(-\frac{1}{4}a^{3}bc^{2}\right)^{2}.

$$\left(-\frac{1}{4}\right)^{2}\left(a^{3}\right)^{2}b^{2}\left(c^{2}\right)^{2}$$

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

$$\left(-\frac{1}{4}\right)^{2}a^{6}b^{2}\left(c^{2}\right)^{2}$$

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

$$\left(-\frac{1}{4}\right)^{2}a^{6}b^{2}c^{4}$$

Calculate -\frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\frac{1}{16}a^{6}b^{2}c^{4}$$

Expand

$$\frac{b^{2}c^{4}a^{6}}{16}$$

Solution Steps

Combine \frac{5}{4}a^{3}bc^{2} and -a^{3}bc^{2} to get \frac{1}{4}a^{3}bc^{2}.

$$\left(\frac{1}{4}a^{3}bc^{2}-\frac{1}{2}a^{3}bc^{2}\right)^{2}$$

Combine \frac{1}{4}a^{3}bc^{2} and -\frac{1}{2}a^{3}bc^{2} to get -\frac{1}{4}a^{3}bc^{2}.

$$\left(-\frac{1}{4}a^{3}bc^{2}\right)^{2}$$

Expand \left(-\frac{1}{4}a^{3}bc^{2}\right)^{2}.

$$\left(-\frac{1}{4}\right)^{2}\left(a^{3}\right)^{2}b^{2}\left(c^{2}\right)^{2}$$

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

$$\left(-\frac{1}{4}\right)^{2}a^{6}b^{2}\left(c^{2}\right)^{2}$$

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

$$\left(-\frac{1}{4}\right)^{2}a^{6}b^{2}c^{4}$$

Calculate -\frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\frac{1}{16}a^{6}b^{2}c^{4}$$