Solve (frac{15a^{2}b^3}{3ab^2})^2(3ab^4/5ab)

$$( \frac { 15 a ^ { 2 } b ^ { 3 } } { 3 a b ^ { 2 } } ) ^ { 2 } ( \frac { 3 a b ^ { 4 } } { 5 a b } )$$

Evaluate

$$15a^{2}b^{5}$$

Solution Steps

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

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

Expand \left(5ab\right)^{2}.

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

Calculate 5 to the power of 2 and get 25.

$$25a^{2}b^{2}\times \frac{3ab^{4}}{5ab}$$

Cancel out ab in both numerator and denominator.

$$25a^{2}b^{2}\times \frac{3b^{3}}{5}$$

Cancel out 5, the greatest common factor in 25 and 5.

$$5\times 3b^{3}a^{2}b^{2}$$

Multiply 5 and 3 to get 15.

$$15b^{3}a^{2}b^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$15b^{5}a^{2}$$

Expand

$$15a^{2}b^{5}$$

Solution Steps

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

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

Expand \left(5ab\right)^{2}.

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

Calculate 5 to the power of 2 and get 25.

$$25a^{2}b^{2}\times \frac{3ab^{4}}{5ab}$$

Cancel out ab in both numerator and denominator.

$$25a^{2}b^{2}\times \frac{3b^{3}}{5}$$

Cancel out 5, the greatest common factor in 25 and 5.

$$5\times 3b^{3}a^{2}b^{2}$$

Multiply 5 and 3 to get 15.

$$15b^{3}a^{2}b^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$15b^{5}a^{2}$$