Solve (frac{2^{-3}5^{4}5^{-3}3^{-7}}{5^23^45^-32^-5})

$$( \frac { 2 ^ { - 3 } 5 ^ { 4 } 5 ^ { - 3 } 3 ^ { - 7 } } { 5 ^ { 2 } 3 ^ { 4 } 5 ^ { - 3 } 2 ^ { - 5 } } )$$

Evaluate

$$\frac{100}{177147}\approx 0.000564503$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and -3 to get 1.

$$\frac{2^{-3}\times 5^{1}\times 3^{-7}}{5^{2}\times 3^{4}\times 5^{-3}\times 2^{-5}}$$

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

$$\frac{2^{-3}\times 5^{1}\times 3^{-7}}{5^{-1}\times 3^{4}\times 2^{-5}}$$

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

$$\frac{2^{2}\times 3^{-7}\times 5^{2}}{3^{4}}$$

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

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

Calculate 2 to the power of 2 and get 4.

$$\frac{4\times 5^{2}}{3^{11}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{4\times 25}{3^{11}}$$

Multiply 4 and 25 to get 100.

$$\frac{100}{3^{11}}$$

Calculate 3 to the power of 11 and get 177147.

$$\frac{100}{177147}$$

Factor

$$\frac{2 ^ {2} \cdot 5 ^ {2}}{3 ^ {11}} = 0.0005645029269476762$$