Solve (-4a^2b)^2*(-1/ab^2)^3

$$( - 4 a ^ { 2 } b ) ^ { 2 } \times ( - \frac { 1 } { a b ^ { 2 } } ) ^ { 3 }$$

Evaluate

$$-\frac{16a}{b^{4}}$$

Solution Steps

Expand \left(-4a^{2}b\right)^{2}.

$$\left(-4\right)^{2}\left(a^{2}\right)^{2}b^{2}\left(-\frac{1}{ab^{2}}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\left(-4\right)^{2}a^{4}b^{2}\left(-\frac{1}{ab^{2}}\right)^{3}$$

Calculate -4 to the power of 2 and get 16.

$$16a^{4}b^{2}\left(-\frac{1}{ab^{2}}\right)^{3}$$

Expand \left(-\frac{1}{ab^{2}}\right)^{3}.

$$16a^{4}b^{2}\left(-1\right)^{3}\times \left(\frac{1}{ab^{2}}\right)^{3}$$

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

$$16a^{4}b^{2}\left(-1\right)\times \left(\frac{1}{ab^{2}}\right)^{3}$$

To raise \frac{1}{ab^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$16a^{4}b^{2}\left(-1\right)\times \frac{1^{3}}{\left(ab^{2}\right)^{3}}$$

Multiply 16 and -1 to get -16.

$$-16a^{4}b^{2}\times \frac{1^{3}}{\left(ab^{2}\right)^{3}}$$

Calculate 1 to the power of 3 and get 1.

$$-16a^{4}b^{2}\times \frac{1}{\left(ab^{2}\right)^{3}}$$

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

$$-16a^{4}b^{2}\times \frac{1}{a^{3}\left(b^{2}\right)^{3}}$$

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

$$-16a^{4}b^{2}\times \frac{1}{a^{3}b^{6}}$$

Express -16\times \frac{1}{a^{3}b^{6}} as a single fraction.

$$\frac{-16}{a^{3}b^{6}}a^{4}b^{2}$$

Express \frac{-16}{a^{3}b^{6}}a^{4} as a single fraction.

$$\frac{-16a^{4}}{a^{3}b^{6}}b^{2}$$

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

$$\frac{-16a}{b^{6}}b^{2}$$

Express \frac{-16a}{b^{6}}b^{2} as a single fraction.

$$\frac{-16ab^{2}}{b^{6}}$$

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

$$\frac{-16a}{b^{4}}$$

Expand

$$-\frac{16a}{b^{4}}$$

Solution Steps

Expand \left(-4a^{2}b\right)^{2}.

$$\left(-4\right)^{2}\left(a^{2}\right)^{2}b^{2}\left(-\frac{1}{ab^{2}}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\left(-4\right)^{2}a^{4}b^{2}\left(-\frac{1}{ab^{2}}\right)^{3}$$

Calculate -4 to the power of 2 and get 16.

$$16a^{4}b^{2}\left(-\frac{1}{ab^{2}}\right)^{3}$$

Expand \left(-\frac{1}{ab^{2}}\right)^{3}.

$$16a^{4}b^{2}\left(-1\right)^{3}\times \left(\frac{1}{ab^{2}}\right)^{3}$$

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

$$16a^{4}b^{2}\left(-1\right)\times \left(\frac{1}{ab^{2}}\right)^{3}$$

To raise \frac{1}{ab^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$16a^{4}b^{2}\left(-1\right)\times \frac{1^{3}}{\left(ab^{2}\right)^{3}}$$

Multiply 16 and -1 to get -16.

$$-16a^{4}b^{2}\times \frac{1^{3}}{\left(ab^{2}\right)^{3}}$$

Calculate 1 to the power of 3 and get 1.

$$-16a^{4}b^{2}\times \frac{1}{\left(ab^{2}\right)^{3}}$$

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

$$-16a^{4}b^{2}\times \frac{1}{a^{3}\left(b^{2}\right)^{3}}$$

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

$$-16a^{4}b^{2}\times \frac{1}{a^{3}b^{6}}$$

Express -16\times \frac{1}{a^{3}b^{6}} as a single fraction.

$$\frac{-16}{a^{3}b^{6}}a^{4}b^{2}$$

Express \frac{-16}{a^{3}b^{6}}a^{4} as a single fraction.

$$\frac{-16a^{4}}{a^{3}b^{6}}b^{2}$$

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

$$\frac{-16a}{b^{6}}b^{2}$$

Express \frac{-16a}{b^{6}}b^{2} as a single fraction.

$$\frac{-16ab^{2}}{b^{6}}$$

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

$$\frac{-16a}{b^{4}}$$