Calculate the Fraction: Finding the Value of 1/2^9

$2^{-9}$ means reciprocal and equals $\frac{1}{512}$ (positive). $-2^9$ means negative and equals $-512$. The negative exponent creates a fraction, not a negative number!

This uses the negative exponent rule: $a^{-n} = \frac{1}{a^n}$. Since we have $\frac{1}{2^9}$, we can write it as $2^{-9}$ by moving the base to the other side and flipping the exponent sign.

No! $2^{-9}$ means positive 2 raised to negative 9 = $\frac{1}{512}$. $(-2)^9$ means negative 2 raised to positive 9 = $-512$. The placement of parentheses matters!

Build up step by step: $2^1 = 2$, $2^2 = 4$, $2^3 = 8$, $2^4 = 16$, $2^5 = 32$, $2^6 = 64$, $2^7 = 128$, $2^8 = 256$, $2^9 = 512$. Each step doubles the previous result!

You could calculate $\frac{1}{512} = 0.001953125$, but $2^{-9}$ is the most precise form. Unless specifically asked for a decimal, the exponential form is preferred in mathematics.