Solve frac{(5^{-3})^{2}*(10)}{(3^-2)^-3*(5^4)^-2}

$$\frac { ( 5 ^ { - 3 } ) ^ { 2 } \times ( 10 ) } { ( 3 ^ { - 2 } ) ^ { - 3 } \times ( 5 ^ { 4 } ) ^ { - 2 } }$$

Evaluate

$$\frac{250}{729}\approx 0.342935528$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -3 and 2 to get -6.

$$\frac{5^{-6}\times 10}{\left(3^{-2}\right)^{-3}\times \left(5^{4}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply -2 and -3 to get 6.

$$\frac{5^{-6}\times 10}{3^{6}\times \left(5^{4}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -2 to get -8.

$$\frac{5^{-6}\times 10}{3^{6}\times 5^{-8}}$$

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

$$\frac{10\times 5^{2}}{3^{6}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{10\times 25}{3^{6}}$$

Multiply 10 and 25 to get 250.

$$\frac{250}{3^{6}}$$

Calculate 3 to the power of 6 and get 729.

$$\frac{250}{729}$$

Factor

$$\frac{2 \cdot 5 ^ {3}}{3 ^ {6}} = 0.3429355281207133$$