Solve 0-2(-a^{2}bc)^2div1/2a(bc)^3-(-abc)^3*(-abc)^2

$$0 - 2 ( - a ^ { 2 } b c ) ^ { 2 } \div \frac { 1 } { 2 } a ( b c ) ^ { 3 } - ( - a b c ) ^ { 3 } \cdot ( - a b c ) ^ { 2 }$$

Evaluate

$$-3\left(abc\right)^{5}$$

Solution Steps

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

$$0-\frac{2\left(\left(-a^{2}\right)bc\right)^{2}}{\frac{1}{2}}a\left(bc\right)^{3}-\left(\left(-a\right)bc\right)^{5}$$

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

$$0-\frac{2\left(-a^{2}\right)^{2}b^{2}c^{2}}{\frac{1}{2}}a\left(bc\right)^{3}-\left(\left(-a\right)bc\right)^{5}$$

Calculate -a^{2} to the power of 2 and get \left(a^{2}\right)^{2}.

$$0-\frac{2\left(a^{2}\right)^{2}b^{2}c^{2}}{\frac{1}{2}}a\left(bc\right)^{3}-\left(\left(-a\right)bc\right)^{5}$$

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

$$0-\frac{2a^{4}b^{2}c^{2}}{\frac{1}{2}}a\left(bc\right)^{3}-\left(\left(-a\right)bc\right)^{5}$$

Divide 2a^{4}b^{2}c^{2} by \frac{1}{2} by multiplying 2a^{4}b^{2}c^{2} by the reciprocal of \frac{1}{2}.

$$0-2a^{4}b^{2}c^{2}\times 2a\left(bc\right)^{3}-\left(\left(-a\right)bc\right)^{5}$$

Multiply 2 and 2 to get 4.

$$0-4a^{4}b^{2}c^{2}a\left(bc\right)^{3}-\left(\left(-a\right)bc\right)^{5}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$0-4a^{5}b^{2}c^{2}\left(bc\right)^{3}-\left(\left(-a\right)bc\right)^{5}$$

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

$$0-4a^{5}b^{2}c^{2}b^{3}c^{3}-\left(\left(-a\right)bc\right)^{5}$$

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

$$0-4a^{5}b^{5}c^{2}c^{3}-\left(\left(-a\right)bc\right)^{5}$$

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

$$0-4a^{5}b^{5}c^{5}-\left(\left(-a\right)bc\right)^{5}$$

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

$$0-4a^{5}b^{5}c^{5}-\left(-a\right)^{5}b^{5}c^{5}$$

Anything plus zero gives itself.

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

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

$$-4a^{5}b^{5}c^{5}-\left(-1\right)^{5}a^{5}b^{5}c^{5}$$

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

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

Multiply -1 and -1 to get 1.

$$-4a^{5}b^{5}c^{5}+a^{5}b^{5}c^{5}$$

Combine -4a^{5}b^{5}c^{5} and a^{5}b^{5}c^{5} to get -3a^{5}b^{5}c^{5}.

$$-3a^{5}b^{5}c^{5}$$

Expand

$$-3\left(abc\right)^{5}$$

Solution Steps

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

$$0-\frac{2\left(\left(-a^{2}\right)bc\right)^{2}}{\frac{1}{2}}a\left(bc\right)^{3}-\left(\left(-a\right)bc\right)^{5}$$

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

$$0-\frac{2\left(-a^{2}\right)^{2}b^{2}c^{2}}{\frac{1}{2}}a\left(bc\right)^{3}-\left(\left(-a\right)bc\right)^{5}$$

Calculate -a^{2} to the power of 2 and get \left(a^{2}\right)^{2}.

$$0-\frac{2\left(a^{2}\right)^{2}b^{2}c^{2}}{\frac{1}{2}}a\left(bc\right)^{3}-\left(\left(-a\right)bc\right)^{5}$$

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

$$0-\frac{2a^{4}b^{2}c^{2}}{\frac{1}{2}}a\left(bc\right)^{3}-\left(\left(-a\right)bc\right)^{5}$$

Divide 2a^{4}b^{2}c^{2} by \frac{1}{2} by multiplying 2a^{4}b^{2}c^{2} by the reciprocal of \frac{1}{2}.

$$0-2a^{4}b^{2}c^{2}\times 2a\left(bc\right)^{3}-\left(\left(-a\right)bc\right)^{5}$$

Multiply 2 and 2 to get 4.

$$0-4a^{4}b^{2}c^{2}a\left(bc\right)^{3}-\left(\left(-a\right)bc\right)^{5}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$0-4a^{5}b^{2}c^{2}\left(bc\right)^{3}-\left(\left(-a\right)bc\right)^{5}$$

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

$$0-4a^{5}b^{2}c^{2}b^{3}c^{3}-\left(\left(-a\right)bc\right)^{5}$$

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

$$0-4a^{5}b^{5}c^{2}c^{3}-\left(\left(-a\right)bc\right)^{5}$$

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

$$0-4a^{5}b^{5}c^{5}-\left(\left(-a\right)bc\right)^{5}$$

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

$$0-4a^{5}b^{5}c^{5}-\left(-a\right)^{5}b^{5}c^{5}$$

Anything plus zero gives itself.

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

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

$$-4a^{5}b^{5}c^{5}-\left(-1\right)^{5}a^{5}b^{5}c^{5}$$

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

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

Multiply -1 and -1 to get 1.

$$-4a^{5}b^{5}c^{5}+a^{5}b^{5}c^{5}$$

Combine -4a^{5}b^{5}c^{5} and a^{5}b^{5}c^{5} to get -3a^{5}b^{5}c^{5}.

$$-3a^{5}b^{5}c^{5}$$