Complete the Expression: (3×4) Raised to Power (3x+1)

Insert the corresponding expression:

(3×4)3x+1= \left(3\times4\right)^{3x+1}=

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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 together.
00:12 To open parentheses with multiplication and an exponent outside,
00:16 we raise each factor inside to that power.
00:20 Now, let's apply this formula to our exercise.
00:24 Notice that the exponent has both addition and power N.
00:28 So we raise each factor to this power, step by step.
00:32 And that's how we find the solution!

Step-by-step written solution

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1

Understand the problem

Insert the corresponding expression:

(3×4)3x+1= \left(3\times4\right)^{3x+1}=

2

Step-by-step solution

To solve this problem, we will apply the power of a product rule.

  • Step 1: Identify the given expression (3×4)3x+1(3 \times 4)^{3x+1}.

  • Step 2: Apply the power of a product rule: (ab)n=an×bn(ab)^n = a^n \times b^n.

  • Step 3: Rewrite the expression using the rule:

By applying (3×4)3x+1=33x+1×43x+1(3 \times 4)^{3x+1} = 3^{3x+1} \times 4^{3x+1}, we distribute the exponent to each base within the parentheses.

Therefore, the correct expression is 33x+1×43x+13^{3x+1} \times 4^{3x+1}.

3

Final Answer

33x+1×43x+1 3^{3x+1}\times4^{3x+1}

Practice Quiz

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

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