Solve (-ab^2)^2div(-ab^2)^5

$$( - a b ^ { 2 } ) ^ { 2 } \div ( - a b ^ { 2 } ) ^ { 5 }$$

Evaluate

$$-\frac{1}{a^{3}b^{6}}$$

Solution Steps

Rewrite \left(\left(-a\right)b^{2}\right)^{5} as \left(\left(-a\right)b^{2}\right)^{2}\left(\left(-a\right)b^{2}\right)^{3}. Cancel out \left(\left(-a\right)b^{2}\right)^{2} in both numerator and denominator.

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

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

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

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

$$\frac{1}{\left(-a\right)^{3}b^{6}}$$

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

$$\frac{1}{\left(-1\right)^{3}a^{3}b^{6}}$$

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

$$\frac{1}{-a^{3}b^{6}}$$

Expand

$$-\frac{1}{a^{3}b^{6}}$$

Solution Steps

Rewrite \left(\left(-a\right)b^{2}\right)^{5} as \left(\left(-a\right)b^{2}\right)^{2}\left(\left(-a\right)b^{2}\right)^{3}. Cancel out \left(\left(-a\right)b^{2}\right)^{2} in both numerator and denominator.

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

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

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

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

$$\frac{1}{\left(-a\right)^{3}b^{6}}$$

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

$$\frac{1}{\left(-1\right)^{3}a^{3}b^{6}}$$

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

$$\frac{1}{-a^{3}b^{6}}$$