Solve a^7b^6diva^5b/3c*(3c/b)^2

$$a ^ { 7 } b ^ { 6 } \div \frac { a ^ { 5 } b } { 3 c } \times ( \frac { 3 c } { b } ) ^ { 2 }$$

Evaluate

$$27a^{2}\left(bc\right)^{3}$$

Solution Steps

Divide a^{7}b^{6} by \frac{a^{5}b}{3c} by multiplying a^{7}b^{6} by the reciprocal of \frac{a^{5}b}{3c}.

$$\frac{a^{7}b^{6}\times 3c}{a^{5}b}\times \left(\frac{3c}{b}\right)^{2}$$

Cancel out ba^{5} in both numerator and denominator.

$$3ca^{2}b^{5}\times \left(\frac{3c}{b}\right)^{2}$$

To raise \frac{3c}{b} to a power, raise both numerator and denominator to the power and then divide.

$$3ca^{2}b^{5}\times \frac{\left(3c\right)^{2}}{b^{2}}$$

Express 3\times \frac{\left(3c\right)^{2}}{b^{2}} as a single fraction.

$$\frac{3\times \left(3c\right)^{2}}{b^{2}}ca^{2}b^{5}$$

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

$$\frac{3\times 3^{2}c^{2}}{b^{2}}ca^{2}b^{5}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{3\times 9c^{2}}{b^{2}}ca^{2}b^{5}$$

Multiply 3 and 9 to get 27.

$$\frac{27c^{2}}{b^{2}}ca^{2}b^{5}$$

Express \frac{27c^{2}}{b^{2}}c as a single fraction.

$$\frac{27c^{2}c}{b^{2}}a^{2}b^{5}$$

Express \frac{27c^{2}c}{b^{2}}a^{2} as a single fraction.

$$\frac{27c^{2}ca^{2}}{b^{2}}b^{5}$$

Express \frac{27c^{2}ca^{2}}{b^{2}}b^{5} as a single fraction.

$$\frac{27c^{2}ca^{2}b^{5}}{b^{2}}$$

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

$$27ca^{2}c^{2}b^{3}$$

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

$$27c^{3}a^{2}b^{3}$$

Expand

$$27a^{2}\left(bc\right)^{3}$$

Solution Steps

Divide a^{7}b^{6} by \frac{a^{5}b}{3c} by multiplying a^{7}b^{6} by the reciprocal of \frac{a^{5}b}{3c}.

$$\frac{a^{7}b^{6}\times 3c}{a^{5}b}\times \left(\frac{3c}{b}\right)^{2}$$

Cancel out ba^{5} in both numerator and denominator.

$$3ca^{2}b^{5}\times \left(\frac{3c}{b}\right)^{2}$$

To raise \frac{3c}{b} to a power, raise both numerator and denominator to the power and then divide.

$$3ca^{2}b^{5}\times \frac{\left(3c\right)^{2}}{b^{2}}$$

Express 3\times \frac{\left(3c\right)^{2}}{b^{2}} as a single fraction.

$$\frac{3\times \left(3c\right)^{2}}{b^{2}}ca^{2}b^{5}$$

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

$$\frac{3\times 3^{2}c^{2}}{b^{2}}ca^{2}b^{5}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{3\times 9c^{2}}{b^{2}}ca^{2}b^{5}$$

Multiply 3 and 9 to get 27.

$$\frac{27c^{2}}{b^{2}}ca^{2}b^{5}$$

Express \frac{27c^{2}}{b^{2}}c as a single fraction.

$$\frac{27c^{2}c}{b^{2}}a^{2}b^{5}$$

Express \frac{27c^{2}c}{b^{2}}a^{2} as a single fraction.

$$\frac{27c^{2}ca^{2}}{b^{2}}b^{5}$$

Express \frac{27c^{2}ca^{2}}{b^{2}}b^{5} as a single fraction.

$$\frac{27c^{2}ca^{2}b^{5}}{b^{2}}$$

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

$$27ca^{2}c^{2}b^{3}$$

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

$$27c^{3}a^{2}b^{3}$$