Calculate 7^(-4): Evaluating Negative Integer Exponents

7−4=? 7^{-4}=\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 together.
00:07 Using the power laws, a number A raised to the power of negative N
00:12 is the same as one divided by A raised to the power of N.
00:17 So, let's apply this rule: it changes numbers to fractions and back.
00:23 We get one divided by seven raised to the power of four.
00:28 Now, let's solve seven raised to the power of four using these laws.
00:34 And there you go, that's the solution!

Step-by-step written solution

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1

Understand the problem

7−4=? 7^{-4}=\text{?}

2

Step-by-step solution

We must first remind ourselves of the negative exponent rule:

a−n=1an a^{-n}=\frac{1}{a^n} When applied to given the expression we obtain the following:

7−4=174=12401 7^{-4}=\frac{1}{7^4}=\frac{1}{2401}

Therefore, the correct answer is option C.

3

Final Answer

12401 \frac{1}{2401}

Practice Quiz

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

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