Solve (frac{a^{4}b^{5}c}{a^{2}b^{3}c})^{2}[frac{(a^{3}b^2)^4c^5}{ab^6c}]=

$$( \frac { a ^ { 4 } b ^ { 5 } c } { a ^ { 2 } b ^ { 3 } c } ) ^ { 2 } [ \frac { ( a ^ { 3 } b ^ { 2 } ) ^ { 4 } c ^ { 5 } } { a b ^ { 6 } c } ] =$$

Evaluate

$$c^{4}b^{6}a^{15}$$

Solution Steps

Cancel out ca^{2}b^{3} in both numerator and denominator.

$$\left(a^{2}b^{2}\right)^{2}\times \frac{\left(a^{3}b^{2}\right)^{4}c^{5}}{ab^{6}c}$$

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

$$\left(a^{2}\right)^{2}\left(b^{2}\right)^{2}\times \frac{\left(a^{3}b^{2}\right)^{4}c^{5}}{ab^{6}c}$$

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

$$a^{4}\left(b^{2}\right)^{2}\times \frac{\left(a^{3}b^{2}\right)^{4}c^{5}}{ab^{6}c}$$

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

$$a^{4}b^{4}\times \frac{\left(a^{3}b^{2}\right)^{4}c^{5}}{ab^{6}c}$$

Cancel out c in both numerator and denominator.

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

Expand \left(b^{2}a^{3}\right)^{4}.

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

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

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

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

$$a^{4}b^{4}\times \frac{c^{4}b^{8}a^{12}}{ab^{6}}$$

Cancel out ab^{6} in both numerator and denominator.

$$a^{4}b^{4}b^{2}c^{4}a^{11}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$a^{4}b^{6}c^{4}a^{11}$$

To multiply powers of the same base, add their exponents. Add 4 and 11 to get 15.

$$a^{15}b^{6}c^{4}$$

Expand

$$c^{4}b^{6}a^{15}$$

Solution Steps

Cancel out ca^{2}b^{3} in both numerator and denominator.

$$\left(a^{2}b^{2}\right)^{2}\times \frac{\left(a^{3}b^{2}\right)^{4}c^{5}}{ab^{6}c}$$

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

$$\left(a^{2}\right)^{2}\left(b^{2}\right)^{2}\times \frac{\left(a^{3}b^{2}\right)^{4}c^{5}}{ab^{6}c}$$

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

$$a^{4}\left(b^{2}\right)^{2}\times \frac{\left(a^{3}b^{2}\right)^{4}c^{5}}{ab^{6}c}$$

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

$$a^{4}b^{4}\times \frac{\left(a^{3}b^{2}\right)^{4}c^{5}}{ab^{6}c}$$

Cancel out c in both numerator and denominator.

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

Expand \left(b^{2}a^{3}\right)^{4}.

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

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

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

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

$$a^{4}b^{4}\times \frac{c^{4}b^{8}a^{12}}{ab^{6}}$$

Cancel out ab^{6} in both numerator and denominator.

$$a^{4}b^{4}b^{2}c^{4}a^{11}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$a^{4}b^{6}c^{4}a^{11}$$

To multiply powers of the same base, add their exponents. Add 4 and 11 to get 15.

$$a^{15}b^{6}c^{4}$$