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

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

Evaluate

$$b^{3}a^{6}$$

Solution Steps

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

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

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

$$\frac{a^{6}b^{3}}{ab^{4}}\times \frac{a^{2}b^{5}}{ab}$$

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

$$\frac{a^{5}}{b}\times \frac{a^{2}b^{5}}{ab}$$

Cancel out ab in both numerator and denominator.

$$\frac{a^{5}}{b}ab^{4}$$

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

$$\frac{a^{5}a}{b}b^{4}$$

Express \frac{a^{5}a}{b}b^{4} as a single fraction.

$$\frac{a^{5}ab^{4}}{b}$$

Cancel out b in both numerator and denominator.

$$ab^{3}a^{5}$$

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

$$a^{6}b^{3}$$

Expand

$$b^{3}a^{6}$$

Solution Steps

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

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

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

$$\frac{a^{6}b^{3}}{ab^{4}}\times \frac{a^{2}b^{5}}{ab}$$

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

$$\frac{a^{5}}{b}\times \frac{a^{2}b^{5}}{ab}$$

Cancel out ab in both numerator and denominator.

$$\frac{a^{5}}{b}ab^{4}$$

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

$$\frac{a^{5}a}{b}b^{4}$$

Express \frac{a^{5}a}{b}b^{4} as a single fraction.

$$\frac{a^{5}ab^{4}}{b}$$

Cancel out b in both numerator and denominator.

$$ab^{3}a^{5}$$

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

$$a^{6}b^{3}$$