Solve (8a^{6}b^3)^2div(-2a^-2b)^3

$$( 8 a ^ { 6 } b ^ { 3 } ) ^ { 2 } \div ( - 2 a ^ { - 2 } b ) ^ { 3 }$$

Evaluate

$$-8b^{3}a^{18}$$

Solution Steps

Expand \left(8a^{6}b^{3}\right)^{2}.

$$\frac{8^{2}\left(a^{6}\right)^{2}\left(b^{3}\right)^{2}}{\left(-2a^{-2}b\right)^{3}}$$

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

$$\frac{8^{2}a^{12}\left(b^{3}\right)^{2}}{\left(-2a^{-2}b\right)^{3}}$$

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

$$\frac{8^{2}a^{12}b^{6}}{\left(-2a^{-2}b\right)^{3}}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{64a^{12}b^{6}}{\left(-2a^{-2}b\right)^{3}}$$

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

$$\frac{64a^{12}b^{6}}{\left(-2\right)^{3}\left(a^{-2}\right)^{3}b^{3}}$$

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

$$\frac{64a^{12}b^{6}}{\left(-2\right)^{3}a^{-6}b^{3}}$$

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

$$\frac{64a^{12}b^{6}}{-8a^{-6}b^{3}}$$

Cancel out 8b^{3} in both numerator and denominator.

$$\frac{8b^{3}a^{12}}{-a^{-6}}$$

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

$$\frac{8b^{3}a^{18}}{-1}$$

Anything divided by -1 gives its opposite.

$$-8b^{3}a^{18}$$

Expand

$$-8b^{3}a^{18}$$

Solution Steps

Expand \left(8a^{6}b^{3}\right)^{2}.

$$\frac{8^{2}\left(a^{6}\right)^{2}\left(b^{3}\right)^{2}}{\left(-2a^{-2}b\right)^{3}}$$

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

$$\frac{8^{2}a^{12}\left(b^{3}\right)^{2}}{\left(-2a^{-2}b\right)^{3}}$$

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

$$\frac{8^{2}a^{12}b^{6}}{\left(-2a^{-2}b\right)^{3}}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{64a^{12}b^{6}}{\left(-2a^{-2}b\right)^{3}}$$

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

$$\frac{64a^{12}b^{6}}{\left(-2\right)^{3}\left(a^{-2}\right)^{3}b^{3}}$$

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

$$\frac{64a^{12}b^{6}}{\left(-2\right)^{3}a^{-6}b^{3}}$$

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

$$\frac{64a^{12}b^{6}}{-8a^{-6}b^{3}}$$

Cancel out 8b^{3} in both numerator and denominator.

$$\frac{8b^{3}a^{12}}{-a^{-6}}$$

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

$$\frac{8b^{3}a^{18}}{-1}$$

Anything divided by -1 gives its opposite.

$$-8b^{3}a^{18}$$