Solve 3^-46^2/5^-23^-2

$$\frac { 3 ^ { - 4 } 6 ^ { 2 } } { 5 ^ { - 2 } 3 ^ { - 2 } }$$

Evaluate

$$100$$

Solution Steps

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{6^{2}}{3^{2}\times 5^{-2}}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{36}{3^{2}\times 5^{-2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{36}{9\times 5^{-2}}$$

Calculate 5 to the power of -2 and get \frac{1}{25}.

$$\frac{36}{9\times \frac{1}{25}}$$

Multiply 9 and \frac{1}{25} to get \frac{9}{25}.

$$\frac{36}{\frac{9}{25}}$$

Divide 36 by \frac{9}{25} by multiplying 36 by the reciprocal of \frac{9}{25}.

$$36\times \frac{25}{9}$$

Multiply 36 and \frac{25}{9} to get 100.

$$100$$

Factor

$$2^{2}\times 5^{2}$$