Solve (-7ab^{4}c)^3[(2a^2c)^2]^3

$$( - 7 a b ^ { 4 } c ) ^ { 3 } [ ( 2 a ^ { 2 } c ) ^ { 2 } ] ^ { 3 }$$

Evaluate

$$-21952c^{9}b^{12}a^{15}$$

Solution Steps

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

$$\left(-7ab^{4}c\right)^{3}\times \left(2a^{2}c\right)^{6}$$

Expand \left(-7ab^{4}c\right)^{3}.

$$\left(-7\right)^{3}a^{3}\left(b^{4}\right)^{3}c^{3}\times \left(2a^{2}c\right)^{6}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\left(-7\right)^{3}a^{3}b^{12}c^{3}\times \left(2a^{2}c\right)^{6}$$

Calculate -7 to the power of 3 and get -343.

$$-343a^{3}b^{12}c^{3}\times \left(2a^{2}c\right)^{6}$$

Expand \left(2a^{2}c\right)^{6}.

$$-343a^{3}b^{12}c^{3}\times 2^{6}\left(a^{2}\right)^{6}c^{6}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 6 to get 12.

$$-343a^{3}b^{12}c^{3}\times 2^{6}a^{12}c^{6}$$

Calculate 2 to the power of 6 and get 64.

$$-343a^{3}b^{12}c^{3}\times 64a^{12}c^{6}$$

Multiply -343 and 64 to get -21952.

$$-21952a^{3}b^{12}c^{3}a^{12}c^{6}$$

To multiply powers of the same base, add their exponents. Add 3 and 12 to get 15.

$$-21952a^{15}b^{12}c^{3}c^{6}$$

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

$$-21952a^{15}b^{12}c^{9}$$

Expand

$$-21952c^{9}b^{12}a^{15}$$

Solution Steps

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

$$\left(-7ab^{4}c\right)^{3}\times \left(2a^{2}c\right)^{6}$$

Expand \left(-7ab^{4}c\right)^{3}.

$$\left(-7\right)^{3}a^{3}\left(b^{4}\right)^{3}c^{3}\times \left(2a^{2}c\right)^{6}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\left(-7\right)^{3}a^{3}b^{12}c^{3}\times \left(2a^{2}c\right)^{6}$$

Calculate -7 to the power of 3 and get -343.

$$-343a^{3}b^{12}c^{3}\times \left(2a^{2}c\right)^{6}$$

Expand \left(2a^{2}c\right)^{6}.

$$-343a^{3}b^{12}c^{3}\times 2^{6}\left(a^{2}\right)^{6}c^{6}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 6 to get 12.

$$-343a^{3}b^{12}c^{3}\times 2^{6}a^{12}c^{6}$$

Calculate 2 to the power of 6 and get 64.

$$-343a^{3}b^{12}c^{3}\times 64a^{12}c^{6}$$

Multiply -343 and 64 to get -21952.

$$-21952a^{3}b^{12}c^{3}a^{12}c^{6}$$

To multiply powers of the same base, add their exponents. Add 3 and 12 to get 15.

$$-21952a^{15}b^{12}c^{3}c^{6}$$

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

$$-21952a^{15}b^{12}c^{9}$$