Solve [2^9*(2^2*2)^3]^-3

$$[ 2 ^ { 9 } \cdot ( 2 ^ { 2 } \cdot 2 ) ^ { 3 } ] ^ { - 3 }$$

Evaluate

$$\frac{1}{18014398509481984}=5.551115123 \cdot 10^{-17}$$

Solution Steps

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

$$\left(2^{9}\times \left(2^{3}\right)^{3}\right)^{-3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\left(2^{9}\times 2^{9}\right)^{-3}$$

To multiply powers of the same base, add their exponents. Add 9 and 9 to get 18.

$$\left(2^{18}\right)^{-3}$$

Calculate 2 to the power of 18 and get 262144.

$$262144^{-3}$$

Calculate 262144 to the power of -3 and get \frac{1}{18014398509481984}.

$$\frac{1}{18014398509481984}$$

Factor

$$\frac{1}{2 ^ {54}} = 5.551115123125783 \times 10^{-17}$$