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GCSE indices question

Given that 3^–n = 0.2

find the value of (3⁴)ⁿ

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Original post by VVDOOMVV

Given that 3^–n = 0.2

find the value of (3⁴)ⁿ

Could you write down what

3^n

equals? That will get you started.

you can write 3^-n as (3ⁿ)^-1 or (3^-1)ⁿ...

OP

Original post by Mr M

Could you write down what

3^n

equals? That will get you started.

i believe its 5 but i'm honestly not understanding the next steps?

OP

Original post by the bear

you can write 3^-n as (3ⁿ)^-1 or (3^-1)ⁿ...

Still don't understand where to go from there?

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Original post by VVDOOMVV

i believe its 5 but i'm honestly not understanding the next steps?

It is 5 because

\displaystyle 3^n=\frac{1}{3^{-n}}=\frac{1}{0.2}=5

Now you need to apply the rule of indices that

\displaystyle (a^b)^c = a^{bc}

.

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Original post by jpxw

...

Please read the Forum Rules at the top of the Maths Forum. Full solutions are not permitted. We just give hints to move people forward in their learning.

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Original post by jacobusargentum

3^n = 5

the recipriocal of .2 is 5

therefore 3^4n= 5^4

the answer is 625

Again, please respect the Forum Rules about not giving full solutions. They can be found at the top of the Maths Forum.

you can write 3^-n = 0.2 as (3ⁿ)^-1 =0.2

power -1 means the reciprocal...

1/(3ⁿ) = 0.2 = 1/5

so (3ⁿ) = 5

Original post by Mr M

Please read the Forum Rules at the top of the Maths Forum. Full solutions are not permitted. We just give hints to move people forward in their learning.

My bad, deleted

OP

Original post by Mr M

It is 5 because

\displaystyle 3^n=\frac{1}{3^{-n}}=\frac{1}{0.2}=5

Now you need to apply the rule of indices that

\displaystyle (a^b)^c = a^{bc}

.

\displaystyle (a^b)^c = a^{bc}

If i apply that to what im given then:

Unparseable latex formula:

\displaystyle (3^4^5)){bc}

or am i missing the point.

(edited 7 years ago)

Study Forum Helper

Original post by VVDOOMVV

\displaystyle (a^b)^c = a^{bc}

If i apply that to what im given then:

Unparseable latex formula:

\displaystyle (3^4^5)){bc}

or am i missing the point.

I think you are struggling with the LaTex so I'm not sure what you are saying,

Note that

(3^4)^n = (3^n)^4

OP

Original post by Mr M

I think you are struggling with the LaTex so I'm not sure what you are saying,

Note that

(3^4)^n = (3^n)^4

sorry but if we use the (a^bc) = (a^b)^c
then wouldn't it be
(3^4x5)

Study Forum Helper

Original post by VVDOOMVV

sorry but if we use the (a^bc) = (a^b)^c
then wouldn't it be
(3^4x5)

No.

3^n = 5

. You seem to be substituting 5 for something else entirely,

OP

Original post by Mr M

No.

3^n = 5

. You seem to be substituting 5 for something else entirely,

I've finally understood it.
(3^4)^n
3n= 5
5^4 = 625

Thank you my friend!

What’s the answer?

625

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