Solve frac{6a^{4}b^5}{ab}*(2ab/a^2b^2)^3

$$\frac { 6 a ^ { 4 } b ^ { 5 } } { a b } \cdot ( \frac { 2 a b } { a ^ { 2 } b ^ { 2 } } ) ^ { 3 }$$

Evaluate

$$48b$$

Solution Steps

Cancel out ab in both numerator and denominator.

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

Cancel out ab in both numerator and denominator.

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

To raise \frac{2}{ab} to a power, raise both numerator and denominator to the power and then divide.

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

Express 6\times \frac{2^{3}}{\left(ab\right)^{3}} as a single fraction.

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

Calculate 2 to the power of 3 and get 8.

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

Multiply 6 and 8 to get 48.

$$\frac{48}{\left(ab\right)^{3}}a^{3}b^{4}$$

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

$$\frac{48}{a^{3}b^{3}}a^{3}b^{4}$$

Express \frac{48}{a^{3}b^{3}}a^{3} as a single fraction.

$$\frac{48a^{3}}{a^{3}b^{3}}b^{4}$$

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

$$\frac{48}{b^{3}}b^{4}$$

Express \frac{48}{b^{3}}b^{4} as a single fraction.

$$\frac{48b^{4}}{b^{3}}$$

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

$$48b$$

Expand

$$48b$$

Solution Steps

Cancel out ab in both numerator and denominator.

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

Cancel out ab in both numerator and denominator.

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

To raise \frac{2}{ab} to a power, raise both numerator and denominator to the power and then divide.

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

Express 6\times \frac{2^{3}}{\left(ab\right)^{3}} as a single fraction.

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

Calculate 2 to the power of 3 and get 8.

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

Multiply 6 and 8 to get 48.

$$\frac{48}{\left(ab\right)^{3}}a^{3}b^{4}$$

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

$$\frac{48}{a^{3}b^{3}}a^{3}b^{4}$$

Express \frac{48}{a^{3}b^{3}}a^{3} as a single fraction.

$$\frac{48a^{3}}{a^{3}b^{3}}b^{4}$$

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

$$\frac{48}{b^{3}}b^{4}$$

Express \frac{48}{b^{3}}b^{4} as a single fraction.

$$\frac{48b^{4}}{b^{3}}$$

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

$$48b$$