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

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

Evaluate

$$\frac{225}{2048}\approx 0.109863281$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -4 and -2 to get -6.

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

To multiply powers of the same base, add their exponents. Add -6 and -5 to get -11.

$$2^{-11}\times 3^{2}\times 5^{2}$$

Calculate 2 to the power of -11 and get \frac{1}{2048}.

$$\frac{1}{2048}\times 3^{2}\times 5^{2}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{1}{2048}\times 9\times 5^{2}$$

Multiply \frac{1}{2048} and 9 to get \frac{9}{2048}.

$$\frac{9}{2048}\times 5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{9}{2048}\times 25$$

Multiply \frac{9}{2048} and 25 to get \frac{225}{2048}.

$$\frac{225}{2048}$$

Factor

$$\frac{3 ^ {2} \cdot 5 ^ {2}}{2 ^ {11}} = 0.10986328125$$