Solve (3^4:30^-3)^-3

$$( 3 ^ { 4 } : 30 ^ { - 3 } ) ^ { - 3 }$$

Evaluate

$$\frac{1}{10460353203000000000}\approx 9.559906636 \cdot 10^{-20}$$

Solution Steps

Calculate 3 to the power of 4 and get 81.

$$\left(\frac{81}{30^{-3}}\right)^{-3}$$

Calculate 30 to the power of -3 and get \frac{1}{27000}.

$$\left(\frac{81}{\frac{1}{27000}}\right)^{-3}$$

Divide 81 by \frac{1}{27000} by multiplying 81 by the reciprocal of \frac{1}{27000}.

$$\left(81\times 27000\right)^{-3}$$

Multiply 81 and 27000 to get 2187000.

$$2187000^{-3}$$

Calculate 2187000 to the power of -3 and get \frac{1}{10460353203000000000}.

$$\frac{1}{10460353203000000000}$$

Factor

$$\frac{1}{2 ^ {9} \cdot 3 ^ {21} \cdot 5 ^ {9}} = 9.559906635974805 \times 10^{-20}$$