Hobbs Bowen
02/04/2024 · Primary School
Evaluate \( 2^{-5} \) and write as a fraction in lowest terms. Write an expression with a positive exponent that equals \( 2^{-n} \) for any whole number \( n \). Submit Question
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Step-by-step Solution
To evaluate \( 2^{-5} \), we can use the property of exponents that states \( a^{-b} = \frac{1}{a^b} \). Therefore, we have:
\[
2^{-5} = \frac{1}{2^5}
\]
Next, we calculate \( 2^5 \):
\[
2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32
\]
Thus, we can write:
\[
2^{-5} = \frac{1}{32}
\]
This fraction is already in its lowest terms.
Now, to write an expression with a positive exponent that equals \( 2^{-n} \) for any whole number \( n \), we can use the same property of exponents:
\[
2^{-n} = \frac{1}{2^n}
\]
So, the expression with a positive exponent that equals \( 2^{-n} \) is:
\[
\frac{1}{2^n}
\]
In summary:
- \( 2^{-5} = \frac{1}{32} \)
- An expression with a positive exponent that equals \( 2^{-n} \) is \( \frac{1}{2^n} \).
Quick Answer
\( 2^{-5} = \frac{1}{32} \)
An expression with a positive exponent that equals \( 2^{-n} \) is \( \frac{1}{2^n} \).
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