Simplify: 4^(2y) × 4^(-5) × 4^(-y) × 4^6 Using Laws of Exponents

42y⋅4−5⋅4−y⋅46= 4^{2y}\cdot4^{-5}\cdot4^{-y}\cdot4^6=

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Step-by-step video solution

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00:00 Simplify the following expression
00:03 When multiplying powers with the same base, add together the exponents
00:07 This formula is relevant for any number of bases
00:13 Let's apply this formula to our exercise
00:17 Let's add together all of the exponents
00:28 Combine the factors
00:38 This is the solution

Step-by-step written solution

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1

Understand the problem

42y⋅4−5⋅4−y⋅46= 4^{2y}\cdot4^{-5}\cdot4^{-y}\cdot4^6=

2

Step-by-step solution

We use the power property to multiply terms with identical bases:

am⋅an=am+n a^m\cdot a^n=a^{m+n}
We apply the property for this problem:

42y⋅4−5⋅4−y⋅46=42y+(−5)+(−y)+6=42y−5−y+6 4^{2y}\cdot4^{-5}\cdot4^{-y}\cdot4^6= 4^{2y+(-5)+(-y)+6}=4^{2y-5-y+6}
We simplify the expression we got in the last step:

42y−5−y+6=4y+1 4^{2y-5-y+6} =4^{y+1}
When we add similar terms in the exponent.

Therefore, the correct answer is option c.

3

Final Answer

4y+1 4^{y+1}

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

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