Solve (-3abc)(-a^2c^3)^2(-5a^2b)=

$$( - 3 a b c ) ( - a ^ { 2 } c ^ { 3 } ) ^ { 2 } ( - 5 a ^ { 2 } b ) =$$

Evaluate

$$15b^{2}\left(ac\right)^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

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

Multiply b and b to get b^{2}.

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

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

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

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

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

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

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

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

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

Multiply -3 and -5 to get 15.

$$15a^{3}b^{2}c^{7}\left(a^{2}\right)^{2}$$

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

$$15a^{3}b^{2}c^{7}a^{4}$$

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

$$15a^{7}b^{2}c^{7}$$

Expand

$$15b^{2}\left(ac\right)^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

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

Multiply b and b to get b^{2}.

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

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

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

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

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

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

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

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

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

Multiply -3 and -5 to get 15.

$$15a^{3}b^{2}c^{7}\left(a^{2}\right)^{2}$$

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

$$15a^{3}b^{2}c^{7}a^{4}$$

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

$$15a^{7}b^{2}c^{7}$$