Solve frac{(a^{-4}6)^-2:6^3}{a^10b^-6}

$$\frac { ( a ^ { - 4 } 6 ) ^ { - 2 } : 6 ^ { 3 } } { a ^ { 10 } b ^ { - 6 } }$$

Evaluate

$$\frac{b^{6}}{7776a^{2}}$$

Solution Steps

Express \frac{\frac{\left(a^{-4}\times 6\right)^{-2}}{6^{3}}}{a^{10}b^{-6}} as a single fraction.

$$\frac{\left(a^{-4}\times 6\right)^{-2}}{6^{3}a^{10}b^{-6}}$$

Expand \left(a^{-4}\times 6\right)^{-2}.

$$\frac{\left(a^{-4}\right)^{-2}\times 6^{-2}}{6^{3}a^{10}b^{-6}}$$

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

$$\frac{a^{8}\times 6^{-2}}{6^{3}a^{10}b^{-6}}$$

Calculate 6 to the power of -2 and get \frac{1}{36}.

$$\frac{a^{8}\times \frac{1}{36}}{6^{3}a^{10}b^{-6}}$$

Calculate 6 to the power of 3 and get 216.

$$\frac{a^{8}\times \frac{1}{36}}{216a^{10}b^{-6}}$$

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

$$\frac{\frac{1}{36}}{216b^{-6}a^{2}}$$

Express \frac{\frac{1}{36}}{216b^{-6}a^{2}} as a single fraction.

$$\frac{1}{36\times 216b^{-6}a^{2}}$$

Multiply 36 and 216 to get 7776.

$$\frac{1}{7776b^{-6}a^{2}}$$

Expand

$$\frac{b^{6}}{7776a^{2}}$$

Solution Steps

Express \frac{\frac{\left(a^{-4}\times 6\right)^{-2}}{6^{3}}}{a^{10}b^{-6}} as a single fraction.

$$\frac{\left(a^{-4}\times 6\right)^{-2}}{6^{3}a^{10}b^{-6}}$$

Expand \left(a^{-4}\times 6\right)^{-2}.

$$\frac{\left(a^{-4}\right)^{-2}\times 6^{-2}}{6^{3}a^{10}b^{-6}}$$

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

$$\frac{a^{8}\times 6^{-2}}{6^{3}a^{10}b^{-6}}$$

Calculate 6 to the power of -2 and get \frac{1}{36}.

$$\frac{a^{8}\times \frac{1}{36}}{6^{3}a^{10}b^{-6}}$$

Calculate 6 to the power of 3 and get 216.

$$\frac{a^{8}\times \frac{1}{36}}{216a^{10}b^{-6}}$$

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

$$\frac{\frac{1}{36}}{216b^{-6}a^{2}}$$

Express \frac{\frac{1}{36}}{216b^{-6}a^{2}} as a single fraction.

$$\frac{1}{36\times 216b^{-6}a^{2}}$$

Multiply 36 and 216 to get 7776.

$$\frac{1}{7776b^{-6}a^{2}}$$