Solve 3(a^{2})^3b^-2c^4/12(ab)^3c

$$3 ( a ^ { 2 } ) ^ { 3 } b ^ { - 2 } c ^ { 4 } / 12 ( a b ) ^ { 3 } c$$

Evaluate

$$\frac{bc^{5}a^{9}}{4}$$

Solution Steps

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

$$\frac{3a^{6}b^{-2}c^{4}}{12}\left(ab\right)^{3}c$$

Divide 3a^{6}b^{-2}c^{4} by 12 to get \frac{1}{4}a^{6}b^{-2}c^{4}.

$$\frac{1}{4}a^{6}b^{-2}c^{4}\left(ab\right)^{3}c$$

Expand \left(ab\right)^{3}.

$$\frac{1}{4}a^{6}b^{-2}c^{4}a^{3}b^{3}c$$

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

$$\frac{1}{4}a^{9}b^{-2}c^{4}b^{3}c$$

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

$$\frac{1}{4}a^{9}b^{1}c^{4}c$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{1}{4}a^{9}b^{1}c^{5}$$

Calculate b to the power of 1 and get b.

$$\frac{1}{4}a^{9}bc^{5}$$

Expand

$$\frac{bc^{5}a^{9}}{4}$$

Solution Steps

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

$$\frac{3a^{6}b^{-2}c^{4}}{12}\left(ab\right)^{3}c$$

Divide 3a^{6}b^{-2}c^{4} by 12 to get \frac{1}{4}a^{6}b^{-2}c^{4}.

$$\frac{1}{4}a^{6}b^{-2}c^{4}\left(ab\right)^{3}c$$

Expand \left(ab\right)^{3}.

$$\frac{1}{4}a^{6}b^{-2}c^{4}a^{3}b^{3}c$$

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

$$\frac{1}{4}a^{9}b^{-2}c^{4}b^{3}c$$

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

$$\frac{1}{4}a^{9}b^{1}c^{4}c$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{1}{4}a^{9}b^{1}c^{5}$$

Calculate b to the power of 1 and get b.

$$\frac{1}{4}a^{9}bc^{5}$$