Solve (-2a^2b)*3/64ab*(-8a^3bc)^2

$$( - 2 a ^ { 2 } b ) \cdot \frac { 3 } { 64 } a b \cdot ( - 8 a ^ { 3 } b c ) ^ { 2 }$$

Evaluate

$$-6c^{2}b^{4}a^{9}$$

Solution Steps

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

$$-2a^{3}b\times \frac{3}{64}b\left(-8a^{3}bc\right)^{2}$$

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

$$-2a^{3}b^{2}\times \frac{3}{64}\left(-8a^{3}bc\right)^{2}$$

Multiply -2 and \frac{3}{64} to get -\frac{3}{32}.

$$-\frac{3}{32}a^{3}b^{2}\left(-8a^{3}bc\right)^{2}$$

Expand \left(-8a^{3}bc\right)^{2}.

$$-\frac{3}{32}a^{3}b^{2}\left(-8\right)^{2}\left(a^{3}\right)^{2}b^{2}c^{2}$$

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

$$-\frac{3}{32}a^{3}b^{2}\left(-8\right)^{2}a^{6}b^{2}c^{2}$$

Calculate -8 to the power of 2 and get 64.

$$-\frac{3}{32}a^{3}b^{2}\times 64a^{6}b^{2}c^{2}$$

Multiply -\frac{3}{32} and 64 to get -6.

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

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

$$-6a^{9}b^{2}b^{2}c^{2}$$

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

$$-6a^{9}b^{4}c^{2}$$

Expand

$$-6c^{2}b^{4}a^{9}$$

Solution Steps

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

$$-2a^{3}b\times \frac{3}{64}b\left(-8a^{3}bc\right)^{2}$$

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

$$-2a^{3}b^{2}\times \frac{3}{64}\left(-8a^{3}bc\right)^{2}$$

Multiply -2 and \frac{3}{64} to get -\frac{3}{32}.

$$-\frac{3}{32}a^{3}b^{2}\left(-8a^{3}bc\right)^{2}$$

Expand \left(-8a^{3}bc\right)^{2}.

$$-\frac{3}{32}a^{3}b^{2}\left(-8\right)^{2}\left(a^{3}\right)^{2}b^{2}c^{2}$$

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

$$-\frac{3}{32}a^{3}b^{2}\left(-8\right)^{2}a^{6}b^{2}c^{2}$$

Calculate -8 to the power of 2 and get 64.

$$-\frac{3}{32}a^{3}b^{2}\times 64a^{6}b^{2}c^{2}$$

Multiply -\frac{3}{32} and 64 to get -6.

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

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

$$-6a^{9}b^{2}b^{2}c^{2}$$

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

$$-6a^{9}b^{4}c^{2}$$