Solve for 4^(-1): Converting Negative Exponent to Reciprocal

Question

4−1=? 4^{-1}=\text{?}

Video Solution

Solution Steps

00:03 Let's solve this problem together.
00:06 Remember, if we have a number, A, raised to the power of negative N.
00:11 And it's not zero, then we can write it as, one divided by A to the power of N.
00:17 Let's see how this applies to our question.
00:21 For example, four to the power of negative one becomes one over four.
00:26 The power negative one, turns into a positive one in the denominator.
00:31 And that's how we find the solution!

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:

4−1=141=14 4^{-1}=\frac{1}{4^1}=\frac{1}{4} We can therefore deduce that the correct answer is option B.

Answer

14 \frac{1}{4}

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Related Subjects

Negative Exponents Exponents and Exponent rules Rules of Exponentiation Combining Powers and Roots Properties of Exponents Exponents - Special Cases

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