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

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

Evaluate

$$\frac{25}{1458}\approx 0.017146776$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -3 and -3 to get -6.

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

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

$$3^{-6}\times 2^{-1}\times 5^{2}$$

Calculate 3 to the power of -6 and get \frac{1}{729}.

$$\frac{1}{729}\times 2^{-1}\times 5^{2}$$

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

$$\frac{1}{729}\times \frac{1}{2}\times 5^{2}$$

Multiply \frac{1}{729} and \frac{1}{2} to get \frac{1}{1458}.

$$\frac{1}{1458}\times 5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{1}{1458}\times 25$$

Multiply \frac{1}{1458} and 25 to get \frac{25}{1458}.

$$\frac{25}{1458}$$

Factor

$$\frac{5 ^ {2}}{2 \cdot 3 ^ {6}} = 0.017146776406035666$$