Solve (a^2*a^-4)/a^5:a^7

$$\frac { ( a ^ { 2 } \cdot a ^ { - 4 } ) } { a ^ { 5 } : a ^ { 7 } }$$

Evaluate

$$1$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and -4 to get -2.

$$\frac{a^{-2}}{\frac{a^{5}}{a^{7}}}$$

Rewrite a^{7} as a^{5}a^{2}. Cancel out a^{5} in both numerator and denominator.

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

Divide a^{-2} by \frac{1}{a^{2}} by multiplying a^{-2} by the reciprocal of \frac{1}{a^{2}}.

$$a^{-2}a^{2}$$

Multiply a^{-2} and a^{2} to get 1.

$$1$$

Factor

$$1$$