Solve 2^2/2^4*3^5*4^2/{3^2}

$$\frac{ { 2 }^{ 2 } }{ { 2 }^{ 4 } } \times { 3 }^{ 5 } \times \frac{ { 4 }^{ 2 } }{ { 3 }^{ 2 } }$$

Evaluate

$$108$$

Solution Steps

Rewrite 2^{4} as 2^{2}\times 2^{2}. Cancel out 2^{2} in both numerator and denominator.

$$\frac{1}{2^{2}}\times 3^{5}\times \frac{4^{2}}{3^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{1}{4}\times 3^{5}\times \frac{4^{2}}{3^{2}}$$

Calculate 3 to the power of 5 and get 243.

$$\frac{1}{4}\times 243\times \frac{4^{2}}{3^{2}}$$

Multiply \frac{1}{4} and 243 to get \frac{243}{4}.

$$\frac{243}{4}\times \frac{4^{2}}{3^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{243}{4}\times \frac{16}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{243}{4}\times \frac{16}{9}$$

Multiply \frac{243}{4} times \frac{16}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{243\times 16}{4\times 9}$$

Do the multiplications in the fraction \frac{243\times 16}{4\times 9}.

$$\frac{3888}{36}$$

Divide 3888 by 36 to get 108.

$$108$$

Factor

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