Solve -10(-a^{3}b^{2}c)^{2}*1/5a*(bc)^{3}-(2abc)^3*(-a^2b^2c)^2

$$- 10 ( - a ^ { 3 } b ^ { 2 } c ) ^ { 2 } \cdot \frac { 1 } { 5 } a \cdot ( b c ) ^ { 3 } - ( 2 a b c ) ^ { 3 } \cdot ( - a ^ { 2 } b ^ { 2 } c ) ^ { 2 }$$

Evaluate

$$-10c^{5}\left(ab\right)^{7}$$

Solution Steps

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

$$-10\left(-a^{3}\right)^{2}\left(b^{2}\right)^{2}c^{2}\times \frac{1}{5}a\left(bc\right)^{3}-\left(2abc\right)^{3}\left(\left(-a^{2}\right)b^{2}c\right)^{2}$$

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

$$-10\left(-a^{3}\right)^{2}b^{4}c^{2}\times \frac{1}{5}a\left(bc\right)^{3}-\left(2abc\right)^{3}\left(\left(-a^{2}\right)b^{2}c\right)^{2}$$

Calculate -a^{3} to the power of 2 and get \left(a^{3}\right)^{2}.

$$-10\left(a^{3}\right)^{2}b^{4}c^{2}\times \frac{1}{5}a\left(bc\right)^{3}-\left(2abc\right)^{3}\left(\left(-a^{2}\right)b^{2}c\right)^{2}$$

Multiply -10 and \frac{1}{5} to get -2.

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

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

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

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$-2\left(a^{3}\right)^{2}b^{7}c^{2}ac^{3}-\left(2abc\right)^{3}\left(\left(-a^{2}\right)b^{2}c\right)^{2}$$

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

$$-2\left(a^{3}\right)^{2}b^{7}c^{5}a-\left(2abc\right)^{3}\left(\left(-a^{2}\right)b^{2}c\right)^{2}$$

Expand \left(2abc\right)^{3}.

$$-2\left(a^{3}\right)^{2}b^{7}c^{5}a-2^{3}a^{3}b^{3}c^{3}\left(\left(-a^{2}\right)b^{2}c\right)^{2}$$

Calculate 2 to the power of 3 and get 8.

$$-2\left(a^{3}\right)^{2}b^{7}c^{5}a-8a^{3}b^{3}c^{3}\left(\left(-a^{2}\right)b^{2}c\right)^{2}$$

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

$$-2\left(a^{3}\right)^{2}b^{7}c^{5}a-8a^{3}b^{3}c^{3}\left(-a^{2}\right)^{2}\left(b^{2}\right)^{2}c^{2}$$

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

$$-2\left(a^{3}\right)^{2}b^{7}c^{5}a-8a^{3}b^{3}c^{3}\left(-a^{2}\right)^{2}b^{4}c^{2}$$

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

$$-2\left(a^{3}\right)^{2}b^{7}c^{5}a-8a^{3}b^{3}c^{3}\left(a^{2}\right)^{2}b^{4}c^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$-2\left(a^{3}\right)^{2}b^{7}c^{5}a-8a^{3}b^{7}c^{3}\left(a^{2}\right)^{2}c^{2}$$

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

$$-2\left(a^{3}\right)^{2}b^{7}c^{5}a-8a^{3}b^{7}c^{5}\left(a^{2}\right)^{2}$$

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

$$-2a^{6}b^{7}c^{5}a-8a^{3}b^{7}c^{5}\left(a^{2}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$-2a^{7}b^{7}c^{5}-8a^{3}b^{7}c^{5}\left(a^{2}\right)^{2}$$

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

$$-2a^{7}b^{7}c^{5}-8a^{3}b^{7}c^{5}a^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$-2a^{7}b^{7}c^{5}-8a^{7}b^{7}c^{5}$$

Combine -2a^{7}b^{7}c^{5} and -8a^{7}b^{7}c^{5} to get -10a^{7}b^{7}c^{5}.

$$-10a^{7}b^{7}c^{5}$$

Expand

$$-10c^{5}\left(ab\right)^{7}$$

Solution Steps

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

$$-10\left(-a^{3}\right)^{2}\left(b^{2}\right)^{2}c^{2}\times \frac{1}{5}a\left(bc\right)^{3}-\left(2abc\right)^{3}\left(\left(-a^{2}\right)b^{2}c\right)^{2}$$

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

$$-10\left(-a^{3}\right)^{2}b^{4}c^{2}\times \frac{1}{5}a\left(bc\right)^{3}-\left(2abc\right)^{3}\left(\left(-a^{2}\right)b^{2}c\right)^{2}$$

Calculate -a^{3} to the power of 2 and get \left(a^{3}\right)^{2}.

$$-10\left(a^{3}\right)^{2}b^{4}c^{2}\times \frac{1}{5}a\left(bc\right)^{3}-\left(2abc\right)^{3}\left(\left(-a^{2}\right)b^{2}c\right)^{2}$$

Multiply -10 and \frac{1}{5} to get -2.

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

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

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

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$-2\left(a^{3}\right)^{2}b^{7}c^{2}ac^{3}-\left(2abc\right)^{3}\left(\left(-a^{2}\right)b^{2}c\right)^{2}$$

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

$$-2\left(a^{3}\right)^{2}b^{7}c^{5}a-\left(2abc\right)^{3}\left(\left(-a^{2}\right)b^{2}c\right)^{2}$$

Expand \left(2abc\right)^{3}.

$$-2\left(a^{3}\right)^{2}b^{7}c^{5}a-2^{3}a^{3}b^{3}c^{3}\left(\left(-a^{2}\right)b^{2}c\right)^{2}$$

Calculate 2 to the power of 3 and get 8.

$$-2\left(a^{3}\right)^{2}b^{7}c^{5}a-8a^{3}b^{3}c^{3}\left(\left(-a^{2}\right)b^{2}c\right)^{2}$$

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

$$-2\left(a^{3}\right)^{2}b^{7}c^{5}a-8a^{3}b^{3}c^{3}\left(-a^{2}\right)^{2}\left(b^{2}\right)^{2}c^{2}$$

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

$$-2\left(a^{3}\right)^{2}b^{7}c^{5}a-8a^{3}b^{3}c^{3}\left(-a^{2}\right)^{2}b^{4}c^{2}$$

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

$$-2\left(a^{3}\right)^{2}b^{7}c^{5}a-8a^{3}b^{3}c^{3}\left(a^{2}\right)^{2}b^{4}c^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$-2\left(a^{3}\right)^{2}b^{7}c^{5}a-8a^{3}b^{7}c^{3}\left(a^{2}\right)^{2}c^{2}$$

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

$$-2\left(a^{3}\right)^{2}b^{7}c^{5}a-8a^{3}b^{7}c^{5}\left(a^{2}\right)^{2}$$

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

$$-2a^{6}b^{7}c^{5}a-8a^{3}b^{7}c^{5}\left(a^{2}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$-2a^{7}b^{7}c^{5}-8a^{3}b^{7}c^{5}\left(a^{2}\right)^{2}$$

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

$$-2a^{7}b^{7}c^{5}-8a^{3}b^{7}c^{5}a^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$-2a^{7}b^{7}c^{5}-8a^{7}b^{7}c^{5}$$

Combine -2a^{7}b^{7}c^{5} and -8a^{7}b^{7}c^{5} to get -10a^{7}b^{7}c^{5}.

$$-10a^{7}b^{7}c^{5}$$