Solve [5^-1/3^2]^3]

$$[ \frac { 5 ^ { - 1 } } { 3 ^ { 2 } } ] ^ { 3 } ]$$

Evaluate

$$\frac{1}{91125}\approx 0.000010974$$

Solution Steps

Calculate 5 to the power of -1 and get \frac{1}{5}.

$$\left(\frac{\frac{1}{5}}{3^{2}}\right)^{3}$$

Calculate 3 to the power of 2 and get 9.

$$\left(\frac{\frac{1}{5}}{9}\right)^{3}$$

Express \frac{\frac{1}{5}}{9} as a single fraction.

$$\left(\frac{1}{5\times 9}\right)^{3}$$

Multiply 5 and 9 to get 45.

$$\left(\frac{1}{45}\right)^{3}$$

Calculate \frac{1}{45} to the power of 3 and get \frac{1}{91125}.

$$\frac{1}{91125}$$

Factor

$$\frac{1}{3 ^ {6} \cdot 5 ^ {3}} = 1.0973936899862826 \times 10^{-5}$$