Solve frac{50*a^{3}*(-b^{5})^3}{5^2*(a*b^6)^2}=

$$\frac { 50 \cdot a ^ { 3 } \cdot ( - b ^ { 5 } ) ^ { 3 } } { 5 ^ { 2 } \cdot ( a \cdot b ^ { 6 } ) ^ { 2 } } =$$

Evaluate

$$-2ab^{3}$$

Short Solution Steps

Calculate 5 to the power of 2 and get 25.

$$\frac{50a^{3}\left(-b^{5}\right)^{3}}{25\left(ab^{6}\right)^{2}}$$

Expand \left(ab^{6}\right)^{2}.

$$\frac{50a^{3}\left(-b^{5}\right)^{3}}{25a^{2}\left(b^{6}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\frac{50a^{3}\left(-b^{5}\right)^{3}}{25a^{2}b^{12}}$$

Cancel out 25a^{2} in both numerator and denominator.

$$\frac{2a\left(-b^{5}\right)^{3}}{b^{12}}$$

Expand \left(-b^{5}\right)^{3}.

$$\frac{2a\left(-1\right)^{3}\left(b^{5}\right)^{3}}{b^{12}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{2a\left(-1\right)^{3}b^{15}}{b^{12}}$$

Calculate -1 to the power of 3 and get -1.

$$\frac{2a\left(-1\right)b^{15}}{b^{12}}$$

Multiply 2 and -1 to get -2.

$$\frac{-2ab^{15}}{b^{12}}$$

Cancel out b^{12} in both numerator and denominator.

$$-2ab^{3}$$

Expand

$$-2ab^{3}$$

Short Solution Steps

Calculate 5 to the power of 2 and get 25.

$$\frac{50a^{3}\left(-b^{5}\right)^{3}}{25\left(ab^{6}\right)^{2}}$$

Expand \left(ab^{6}\right)^{2}.

$$\frac{50a^{3}\left(-b^{5}\right)^{3}}{25a^{2}\left(b^{6}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\frac{50a^{3}\left(-b^{5}\right)^{3}}{25a^{2}b^{12}}$$

Cancel out 25a^{2} in both numerator and denominator.

$$\frac{2a\left(-b^{5}\right)^{3}}{b^{12}}$$

Expand \left(-b^{5}\right)^{3}.

$$\frac{2a\left(-1\right)^{3}\left(b^{5}\right)^{3}}{b^{12}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{2a\left(-1\right)^{3}b^{15}}{b^{12}}$$

Calculate -1 to the power of 3 and get -1.

$$\frac{2a\left(-1\right)b^{15}}{b^{12}}$$

Multiply 2 and -1 to get -2.

$$\frac{-2ab^{15}}{b^{12}}$$

Cancel out b^{12} in both numerator and denominator.

$$-2ab^{3}$$