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# If n is an integer and (−3)^{4n}=3^{7n−3}[/m] then n=

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Re: If n is an integer and (−3)^{4n}=3^{7n−3}[/m] then n= [#permalink]
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sony1000
Hi, not clear why is the negative sign removed (−3)^4n, could you explain please....

Since n is an integer then 4n is even thus (−3)^(4n) = 3^(4n).
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Re: If n is an integer and (−3)^{4n}=3^{7n−3}[/m] then n= [#permalink]
Right on.. Thank you.
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Re: If n is an integer and (−3)^{4n}=3^{7n−3}[/m] then n= [#permalink]
Hi, But the stem doesnt say if 'n' is a positive or a negative integer. Then how could we conclude that (-3)^4n = 3^4n ??
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Re: If n is an integer and (−3)^{4n}=3^{7n−3}[/m] then n= [#permalink]
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bedarkaryashas
Hi, But the stem doesnt say if 'n' is a positive or a negative integer. Then how could we conclude that (-3)^4n = 3^4n ??

If a negative number is raised to an EVEN power, the result will always be positive.
For example, (-1)^4 = 1

Now notice that we can rewrite $$(-3)^{4n}$$ as $$((-3)^4)^n$$

So we get: $$(-3)^{4n}=((-3)^4)^n=81^n=(3^4)^n$$

Does that help?
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Re: If n is an integer and (−3)^{4n}=3^{7n−3}[/m] then n= [#permalink]
Hi Brent. Thank you for helping out. But my doubt is: the question steam doesn't state if n is +ve or -ve integer.
Accordingly, if n is a negative integer (assume n= -1) then the equation would be:
(-3)^(4* -1)
i.e. (-3)^ (-4)
i.e. (1/ 81)

What do you think?
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Re: If n is an integer and (−3)^{4n}=3^{7n−3}[/m] then n= [#permalink]
BrentGMATPrepNow
bedarkaryashas
Hi, But the stem doesnt say if 'n' is a positive or a negative integer. Then how could we conclude that (-3)^4n = 3^4n ??

If a negative number is raised to an EVEN power, the result will always be positive.
For example, (-1)^4 = 1

Now notice that we can rewrite $$(-3)^{4n}$$ as $$((-3)^4)^n$$

So we get: $$(-3)^{4n}=((-3)^4)^n=81^n=(3^4)^n$$

Does that help?

Hi Brent. Thank you for helping out. But my doubt is: the question steam doesn't state if n is +ve or -ve integer.
Accordingly, if n is a negative integer (assume n= -1) then the equation would be:
(-3)^(4* -1)
i.e. (-3)^ (-4)
i.e. (1/ 81)

What do you think?
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If n is an integer and (−3)^{4n}=3^{7n−3}[/m] then n= [#permalink]
Top Contributor
bedarkaryashas
BrentGMATPrepNow
bedarkaryashas
Hi, But the stem doesnt say if 'n' is a positive or a negative integer. Then how could we conclude that (-3)^4n = 3^4n ??

If a negative number is raised to an EVEN power, the result will always be positive.
For example, (-1)^4 = 1

Now notice that we can rewrite $$(-3)^{4n}$$ as $$((-3)^4)^n$$

So we get: $$(-3)^{4n}=((-3)^4)^n=81^n=(3^4)^n$$

Does that help?

Hi Brent. Thank you for helping out. But my doubt is: the question steam doesn't state if n is +ve or -ve integer.
Accordingly, if n is a negative integer (assume n= -1) then the equation would be:
(-3)^(4* -1)
i.e. (-3)^ (-4)
i.e. (1/ 81)

What do you think?

But n = -1 is NOT a solution to the given equation, so that has no bearing on the question.

The value of n is implied by the equation $$(−3)^{4n}=3^{7n−3}$$

When we solve the equation for n we get n = 1.

In other words, n cannot equal any other value (negative or positive) other than 1.
If n is an integer and (−3)^{4n}=3^{7n−3}[/m] then n= [#permalink]
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