Solve (a^{2}bc)^4div(ab^2c)^3(abc)^2

$$( a ^ { 2 } b c ) ^ { 4 } \div ( a b ^ { 2 } c ) ^ { 3 } ( a b c ) ^ { 2 }$$

Evaluate

$$c^{3}a^{7}$$

Solution Steps

Expand \left(a^{2}bc\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\frac{a^{8}b^{4}c^{4}}{\left(ab^{2}c\right)^{3}}\left(abc\right)^{2}$$

Expand \left(ab^{2}c\right)^{3}.

$$\frac{a^{8}b^{4}c^{4}}{a^{3}\left(b^{2}\right)^{3}c^{3}}\left(abc\right)^{2}$$

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

$$\frac{a^{8}b^{4}c^{4}}{a^{3}b^{6}c^{3}}\left(abc\right)^{2}$$

Cancel out a^{3}c^{3}b^{4} in both numerator and denominator.

$$\frac{ca^{5}}{b^{2}}\left(abc\right)^{2}$$

Expand \left(abc\right)^{2}.

$$\frac{ca^{5}}{b^{2}}a^{2}b^{2}c^{2}$$

Express \frac{ca^{5}}{b^{2}}a^{2} as a single fraction.

$$\frac{ca^{5}a^{2}}{b^{2}}b^{2}c^{2}$$

Cancel out b^{2} and b^{2}.

$$ca^{5}a^{2}c^{2}$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$ca^{7}c^{2}$$

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

$$c^{3}a^{7}$$

Expand

$$c^{3}a^{7}$$

Solution Steps

Expand \left(a^{2}bc\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\frac{a^{8}b^{4}c^{4}}{\left(ab^{2}c\right)^{3}}\left(abc\right)^{2}$$

Expand \left(ab^{2}c\right)^{3}.

$$\frac{a^{8}b^{4}c^{4}}{a^{3}\left(b^{2}\right)^{3}c^{3}}\left(abc\right)^{2}$$

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

$$\frac{a^{8}b^{4}c^{4}}{a^{3}b^{6}c^{3}}\left(abc\right)^{2}$$

Cancel out a^{3}c^{3}b^{4} in both numerator and denominator.

$$\frac{ca^{5}}{b^{2}}\left(abc\right)^{2}$$

Expand \left(abc\right)^{2}.

$$\frac{ca^{5}}{b^{2}}a^{2}b^{2}c^{2}$$

Express \frac{ca^{5}}{b^{2}}a^{2} as a single fraction.

$$\frac{ca^{5}a^{2}}{b^{2}}b^{2}c^{2}$$

Cancel out b^{2} and b^{2}.

$$ca^{5}a^{2}c^{2}$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$ca^{7}c^{2}$$

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

$$c^{3}a^{7}$$