Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Jan 23, 2024

Find the value of $2^{-5}$ .

STEP 1

Assumptions
1. We need to calculate the value of $2^{-5}$ .
2. Negative exponents indicate the reciprocal of the base raised to the absolute value of the exponent.

STEP 2

The definition of a negative exponent $a^{-n}$ is $\frac{1}{a^n}$ where $a$ is the base and $n$ is the exponent.
$2^{-5} = \frac{1}{2^5}$

STEP 3

Now, calculate the value of $2^5$ .
$2^5 = 2 \times 2 \times 2 \times 2 \times 2$

STEP 4

Multiply the base 2 by itself 5 times.
$2^5 = 32$

STEP 5

Now that we have the value of $2^5$ , we can find the value of $2^{-5}$ by taking the reciprocal.
$2^{-5} = \frac{1}{2^5} = \frac{1}{32}$
The value of $2^{-5}$ is $\frac{1}{32}$ .

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