Solve (a^{6}b^3c)^2div(-3/2a^3bc)^2

$$( a ^ { 6 } b ^ { 3 } c ) ^ { 2 } \div ( - \frac { 3 } { 2 } a ^ { 3 } b c ) ^ { 2 }$$

Evaluate

$$\frac{4b^{4}a^{6}}{9}$$

Solution Steps

Expand \left(a^{6}b^{3}c\right)^{2}.

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

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

$$\frac{a^{12}\left(b^{3}\right)^{2}c^{2}}{\left(-\frac{3}{2}a^{3}bc\right)^{2}}$$

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

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

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

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

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

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

Calculate -\frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$\frac{a^{12}b^{6}c^{2}}{\frac{9}{4}a^{6}b^{2}c^{2}}$$

Cancel out b^{2}c^{2}a^{6} in both numerator and denominator.

$$\frac{b^{4}a^{6}}{\frac{9}{4}}$$

Divide b^{4}a^{6} by \frac{9}{4} by multiplying b^{4}a^{6} by the reciprocal of \frac{9}{4}.

$$\frac{b^{4}a^{6}\times 4}{9}$$

Expand

$$\frac{4b^{4}a^{6}}{9}$$

Solution Steps

Expand \left(a^{6}b^{3}c\right)^{2}.

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

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

$$\frac{a^{12}\left(b^{3}\right)^{2}c^{2}}{\left(-\frac{3}{2}a^{3}bc\right)^{2}}$$

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

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

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

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

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

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

Calculate -\frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$\frac{a^{12}b^{6}c^{2}}{\frac{9}{4}a^{6}b^{2}c^{2}}$$

Cancel out b^{2}c^{2}a^{6} in both numerator and denominator.

$$\frac{b^{4}a^{6}}{\frac{9}{4}}$$

Divide b^{4}a^{6} by \frac{9}{4} by multiplying b^{4}a^{6} by the reciprocal of \frac{9}{4}.

$$\frac{b^{4}a^{6}\times 4}{9}$$