Solve frac{(a^{-7}diva^15)}{a^2}div(a^-6)^4

$$\frac { ( a ^ { - 7 } \div a ^ { 15 } ) } { a ^ { 2 } } \div ( a ^ { - 6 } ) ^ { 4 }$$

Evaluate

$$1$$

Solution Steps

Rewrite a^{15} as a^{-7}a^{22}. Cancel out a^{-7} in both numerator and denominator.

$$\frac{\frac{\frac{1}{a^{22}}}{a^{2}}}{\left(a^{-6}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply -6 and 4 to get -24.

$$\frac{\frac{\frac{1}{a^{22}}}{a^{2}}}{a^{-24}}$$

Express \frac{\frac{\frac{1}{a^{22}}}{a^{2}}}{a^{-24}} as a single fraction.

$$\frac{\frac{1}{a^{22}}}{a^{2}a^{-24}}$$

To multiply powers of the same base, add their exponents. Add 2 and -24 to get -22.

$$\frac{\frac{1}{a^{22}}}{a^{-22}}$$

Express \frac{\frac{1}{a^{22}}}{a^{-22}} as a single fraction.

$$\frac{1}{a^{22}a^{-22}}$$

Multiply a^{22} and a^{-22} to get 1.

$$\frac{1}{1}$$

Anything divided by one gives itself.

$$1$$

Factor

$$1$$