Solve frac{2^{5}*2^{-2}*9*3^{-4}}{2^-2*(2^2)^2*3*3^-3}=

$$\frac { 2 ^ { 5 } \cdot 2 ^ { - 2 } \cdot 9 \cdot 3 ^ { - 4 } } { 2 ^ { - 2 } \cdot ( 2 ^ { 2 } ) ^ { 2 } \cdot 3 \cdot 3 ^ { - 3 } } =$$

Evaluate

$$2$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and -2 to get 3.

$$\frac{2^{3}\times 9\times 3^{-4}}{2^{-2}\times \left(2^{2}\right)^{2}\times 3\times 3^{-3}}$$

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

$$\frac{2^{3}\times 9\times 3^{-4}}{2^{-2}\times 2^{4}\times 3\times 3^{-3}}$$

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

$$\frac{2^{3}\times 9\times 3^{-4}}{2^{2}\times 3\times 3^{-3}}$$

To multiply powers of the same base, add their exponents. Add 1 and -3 to get -2.

$$\frac{2^{3}\times 9\times 3^{-4}}{2^{2}\times 3^{-2}}$$

Cancel out 2^{2} in both numerator and denominator.

$$\frac{2\times 9\times 3^{-4}}{3^{-2}}$$

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

$$\frac{2\times 9}{3^{2}}$$

Multiply 2 and 9 to get 18.

$$\frac{18}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{18}{9}$$

Divide 18 by 9 to get 2.

$$2$$

Factor

$$2$$