Solve (-2a^{3}b^2)^3div(-a^2b)^-2

$$( - 2 a ^ { 3 } b ^ { 2 } ) ^ { 3 } \div ( - a ^ { 2 } b ) ^ { - 2 }$$

Evaluate

$$-8b^{8}a^{13}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{\left(-2\right)^{3}a^{9}\left(b^{2}\right)^{3}}{\left(\left(-a^{2}\right)b\right)^{-2}}$$

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

$$\frac{\left(-2\right)^{3}a^{9}b^{6}}{\left(\left(-a^{2}\right)b\right)^{-2}}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{-8a^{9}b^{6}}{\left(\left(-a^{2}\right)b\right)^{-2}}$$

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

$$\frac{-8a^{9}b^{6}}{\left(-a^{2}\right)^{-2}b^{-2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{-8b^{8}a^{9}}{\left(-a^{2}\right)^{-2}}$$

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

$$\frac{-8b^{8}a^{9}}{\left(-1\right)^{-2}\left(a^{2}\right)^{-2}}$$

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

$$\frac{-8b^{8}a^{9}}{\left(-1\right)^{-2}a^{-4}}$$

Calculate -1 to the power of -2 and get 1.

$$\frac{-8b^{8}a^{9}}{1a^{-4}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$-8b^{8}a^{13}$$

Expand

$$-8b^{8}a^{13}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{\left(-2\right)^{3}a^{9}\left(b^{2}\right)^{3}}{\left(\left(-a^{2}\right)b\right)^{-2}}$$

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

$$\frac{\left(-2\right)^{3}a^{9}b^{6}}{\left(\left(-a^{2}\right)b\right)^{-2}}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{-8a^{9}b^{6}}{\left(\left(-a^{2}\right)b\right)^{-2}}$$

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

$$\frac{-8a^{9}b^{6}}{\left(-a^{2}\right)^{-2}b^{-2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{-8b^{8}a^{9}}{\left(-a^{2}\right)^{-2}}$$

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

$$\frac{-8b^{8}a^{9}}{\left(-1\right)^{-2}\left(a^{2}\right)^{-2}}$$

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

$$\frac{-8b^{8}a^{9}}{\left(-1\right)^{-2}a^{-4}}$$

Calculate -1 to the power of -2 and get 1.

$$\frac{-8b^{8}a^{9}}{1a^{-4}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$-8b^{8}a^{13}$$