Solve frac{(a^{-3}b^-2)^4*a^3b^3}{2ab}

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

Evaluate

$$\frac{1}{2b^{6}a^{10}}$$

Solution Steps

Cancel out ab in both numerator and denominator.

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

Expand \left(a^{-3}b^{-2}\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply -3 and 4 to get -12.

$$\frac{a^{-12}\left(b^{-2}\right)^{4}a^{2}b^{2}}{2}$$

To raise a power to another power, multiply the exponents. Multiply -2 and 4 to get -8.

$$\frac{a^{-12}b^{-8}a^{2}b^{2}}{2}$$

To multiply powers of the same base, add their exponents. Add -12 and 2 to get -10.

$$\frac{a^{-10}b^{-8}b^{2}}{2}$$

To multiply powers of the same base, add their exponents. Add -8 and 2 to get -6.

$$\frac{a^{-10}b^{-6}}{2}$$

Expand

$$\frac{1}{2b^{6}a^{10}}$$

Solution Steps

Cancel out ab in both numerator and denominator.

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

Expand \left(a^{-3}b^{-2}\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply -3 and 4 to get -12.

$$\frac{a^{-12}\left(b^{-2}\right)^{4}a^{2}b^{2}}{2}$$

To raise a power to another power, multiply the exponents. Multiply -2 and 4 to get -8.

$$\frac{a^{-12}b^{-8}a^{2}b^{2}}{2}$$

To multiply powers of the same base, add their exponents. Add -12 and 2 to get -10.

$$\frac{a^{-10}b^{-8}b^{2}}{2}$$

To multiply powers of the same base, add their exponents. Add -8 and 2 to get -6.

$$\frac{a^{-10}b^{-6}}{2}$$