Solve: 4^(-6) × 4 Using Negative Exponent Rules

Insert the corresponding expression:

4−6×4= 4^{-6}\times4=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:08 Let's simplify this problem step by step.
00:12 First, remember: When multiplying powers with the same base, like A,
00:18 we keep the base A and add the exponents, giving us A to the power of N plus M.
00:25 Also, any number to the power of one is just itself.
00:29 So, let's apply this: Our base raised to one stays the same.
00:34 Now, we'll use the second formula.
00:37 Keep the base and add those exponents together.
00:41 Remember: A negative exponent means the reciprocal.
00:45 It becomes its reciprocal raised to the positive exponent N.
00:50 Let's go ahead and apply this rule now.
00:53 Convert to the reciprocal and raise it to the opposite exponent.
00:58 And that's how we solve the problem. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Insert the corresponding expression:

4−6×4= 4^{-6}\times4=

2

Step-by-step solution

To simplify the expression 4−6×44^{-6} \times 4, follow these steps:

  • Step 1: Apply the rule for multiplying powers with the same base, which is am×an=am+na^m \times a^n = a^{m+n}.

  • Step 2: Identify the exponents for the terms. Here, we have 4−64^{-6} and 414^1, implying m=−6m = -6 and n=1n = 1.

  • Step 3: Add the exponents: (−6)+1=−5(-6) + 1 = -5. Thus, we have 4−6×41=4−54^{-6} \times 4^1 = 4^{-5}.

  • Step 4: Recognize that a negative exponent indicates a reciprocal. Therefore, 4−5=1454^{-5} = \frac{1}{4^5}.

Therefore, the solution to the expression 4−6×44^{-6} \times 4 is 145 \frac{1}{4^5} .

3

Final Answer

145 \frac{1}{4^5}

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\( (4^3)^2= \)

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