Calculate 2^(-5): Solving Negative Exponent Expression

2−5=? 2^{-5}=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:04 Let's solve this problem step by step.
00:08 Remember the exponent rule: A raised to the power of N.
00:12 It equals 1 divided by A raised to the power of negative N.
00:18 Now, let's apply this rule to our question.
00:22 The number 2 becomes one-half. The power negative 5 becomes positive 5.
00:28 Remember, a negative times a negative equals a positive.
00:33 And that's how we find the solution!

Step-by-step written solution

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1

Understand the problem

2−5=? 2^{-5}=\text{?}

2

Step-by-step solution

We begin by using the power rule of negative exponents.

a−n=1an a^{-n}=\frac{1}{a^n}

We then apply it to the problem:

2−5=12−(−5)=125 2^{-5}=\frac{1}{2^{-(-5)}}=\frac{1}{2^5}

We can therefore deduce that the correct answer is option A.

3

Final Answer

125 \frac{1}{2^5}

Practice Quiz

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\( 112^0=\text{?} \)

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