Solve [frac{(ab^{2}c^{3})^{2}}{(abc)^{3}}][frac{(7a^{2}b^{4}c^{6})^2}{7a^2b^4c^6}]=

$$[ \frac { ( a b ^ { 2 } c ^ { 3 } ) ^ { 2 } } { ( a b c ) ^ { 3 } } ] [ \frac { ( 7 a ^ { 2 } b ^ { 4 } c ^ { 6 } ) ^ { 2 } } { 7 a ^ { 2 } b ^ { 4 } c ^ { 6 } } ] =$$

Evaluate

$$7ab^{5}c^{9}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 2 to get 1.

$$\frac{\left(ab^{2}c^{3}\right)^{2}}{\left(abc\right)^{3}}\times \left(7a^{2}b^{4}c^{6}\right)^{1}$$

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

$$\frac{a^{2}\left(b^{2}\right)^{2}\left(c^{3}\right)^{2}}{\left(abc\right)^{3}}\times \left(7a^{2}b^{4}c^{6}\right)^{1}$$

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

$$\frac{a^{2}b^{4}\left(c^{3}\right)^{2}}{\left(abc\right)^{3}}\times \left(7a^{2}b^{4}c^{6}\right)^{1}$$

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

$$\frac{a^{2}b^{4}c^{6}}{\left(abc\right)^{3}}\times \left(7a^{2}b^{4}c^{6}\right)^{1}$$

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

$$\frac{a^{2}b^{4}c^{6}}{a^{3}b^{3}c^{3}}\times \left(7a^{2}b^{4}c^{6}\right)^{1}$$

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

$$\frac{bc^{3}}{a}\times \left(7a^{2}b^{4}c^{6}\right)^{1}$$

Calculate 7a^{2}b^{4}c^{6} to the power of 1 and get 7a^{2}b^{4}c^{6}.

$$\frac{bc^{3}}{a}\times 7a^{2}b^{4}c^{6}$$

Express \frac{bc^{3}}{a}\times 7 as a single fraction.

$$\frac{bc^{3}\times 7}{a}a^{2}b^{4}c^{6}$$

Express \frac{bc^{3}\times 7}{a}a^{2} as a single fraction.

$$\frac{bc^{3}\times 7a^{2}}{a}b^{4}c^{6}$$

Cancel out a in both numerator and denominator.

$$7abc^{3}b^{4}c^{6}$$

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

$$7ab^{5}c^{3}c^{6}$$

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

$$7ab^{5}c^{9}$$

Expand

$$7ab^{5}c^{9}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 2 to get 1.

$$\frac{\left(ab^{2}c^{3}\right)^{2}}{\left(abc\right)^{3}}\times \left(7a^{2}b^{4}c^{6}\right)^{1}$$

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

$$\frac{a^{2}\left(b^{2}\right)^{2}\left(c^{3}\right)^{2}}{\left(abc\right)^{3}}\times \left(7a^{2}b^{4}c^{6}\right)^{1}$$

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

$$\frac{a^{2}b^{4}\left(c^{3}\right)^{2}}{\left(abc\right)^{3}}\times \left(7a^{2}b^{4}c^{6}\right)^{1}$$

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

$$\frac{a^{2}b^{4}c^{6}}{\left(abc\right)^{3}}\times \left(7a^{2}b^{4}c^{6}\right)^{1}$$

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

$$\frac{a^{2}b^{4}c^{6}}{a^{3}b^{3}c^{3}}\times \left(7a^{2}b^{4}c^{6}\right)^{1}$$

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

$$\frac{bc^{3}}{a}\times \left(7a^{2}b^{4}c^{6}\right)^{1}$$

Calculate 7a^{2}b^{4}c^{6} to the power of 1 and get 7a^{2}b^{4}c^{6}.

$$\frac{bc^{3}}{a}\times 7a^{2}b^{4}c^{6}$$

Express \frac{bc^{3}}{a}\times 7 as a single fraction.

$$\frac{bc^{3}\times 7}{a}a^{2}b^{4}c^{6}$$

Express \frac{bc^{3}\times 7}{a}a^{2} as a single fraction.

$$\frac{bc^{3}\times 7a^{2}}{a}b^{4}c^{6}$$

Cancel out a in both numerator and denominator.

$$7abc^{3}b^{4}c^{6}$$

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

$$7ab^{5}c^{3}c^{6}$$

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

$$7ab^{5}c^{9}$$