Solve frac{(a^{5}*b^{-4})^3}{(a^8*b^-2)^6}

$$\frac { ( a ^ { 5 } \cdot b ^ { - 4 } ) ^ { 3 } } { ( a ^ { 8 } \cdot b ^ { - 2 } ) ^ { 6 } }$$

Evaluate

$$\frac{1}{a^{33}}$$

Solution Steps

Expand \left(a^{5}b^{-4}\right)^{3}.

$$\frac{\left(a^{5}\right)^{3}\left(b^{-4}\right)^{3}}{\left(a^{8}b^{-2}\right)^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{a^{15}\left(b^{-4}\right)^{3}}{\left(a^{8}b^{-2}\right)^{6}}$$

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

$$\frac{a^{15}b^{-12}}{\left(a^{8}b^{-2}\right)^{6}}$$

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

$$\frac{a^{15}b^{-12}}{\left(a^{8}\right)^{6}\left(b^{-2}\right)^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 6 to get 48.

$$\frac{a^{15}b^{-12}}{a^{48}\left(b^{-2}\right)^{6}}$$

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

$$\frac{a^{15}b^{-12}}{a^{48}b^{-12}}$$

Cancel out b^{-12}a^{15} in both numerator and denominator.

$$\frac{1}{a^{33}}$$

Expand

$$\frac{1}{a^{33}}$$

Solution Steps

Expand \left(a^{5}b^{-4}\right)^{3}.

$$\frac{\left(a^{5}\right)^{3}\left(b^{-4}\right)^{3}}{\left(a^{8}b^{-2}\right)^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{a^{15}\left(b^{-4}\right)^{3}}{\left(a^{8}b^{-2}\right)^{6}}$$

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

$$\frac{a^{15}b^{-12}}{\left(a^{8}b^{-2}\right)^{6}}$$

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

$$\frac{a^{15}b^{-12}}{\left(a^{8}\right)^{6}\left(b^{-2}\right)^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 6 to get 48.

$$\frac{a^{15}b^{-12}}{a^{48}\left(b^{-2}\right)^{6}}$$

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

$$\frac{a^{15}b^{-12}}{a^{48}b^{-12}}$$

Cancel out b^{-12}a^{15} in both numerator and denominator.

$$\frac{1}{a^{33}}$$