Solve -3a^{2}b^{4}*ab^2c^2*(a^5c)^3

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

Evaluate

$$-3c^{5}b^{6}a^{18}$$

Solution Steps

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

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

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

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

Expand \left(a^{5}c\right)^{3}.

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

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$-3a^{3}b^{6}c^{2}a^{15}c^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 15 to get 18.

$$-3a^{18}b^{6}c^{2}c^{3}$$

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

$$-3a^{18}b^{6}c^{5}$$

Expand

$$-3c^{5}b^{6}a^{18}$$

Solution Steps

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

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

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

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

Expand \left(a^{5}c\right)^{3}.

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

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$-3a^{3}b^{6}c^{2}a^{15}c^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 15 to get 18.

$$-3a^{18}b^{6}c^{2}c^{3}$$

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

$$-3a^{18}b^{6}c^{5}$$