# Help with a level indicies!

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Can someone please tell me how to solve these questions,I have no idea what steps I should take,any help would be much appreciated.

7

9

4r

(4r to the power of 5 + 7 =100)

s

(s to the power of -5 is = to 4

simplify: (2√x)

———

8x

(2 root x to the power of 4 over 8x)

7

^{t+6}=49^{2t}^{(7 to the power of t+6 is equal to 49 to power of 2t)}9

^{y+8 }= 27^{y+5}^{(9 to the power of y+8 is equal to 27 to the power of y+5)}4r

^{5 }+ 7=100(4r to the power of 5 + 7 =100)

s

^{-5}=4(s to the power of -5 is = to 4

simplify: (2√x)

^{4}———

8x

(2 root x to the power of 4 over 8x)

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#2

For these you need to make the base numbers equal eachother, so for example 2^2 = 4, so if you had 4^t+1 = 2^t you could do (2^2)^t+1 = 2^2t+2 = 2^t, therefore 2t+2 = t, t = -2. This can be applied to powers of 3 so 2^3 = 8.

For the later questions if x^2 = y then the square root of y is x and vice versa.

For the last one remember that the square root of x is x^0.5.

For the later questions if x^2 = y then the square root of y is x and vice versa.

For the last one remember that the square root of x is x^0.5.

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#4

i just make the bases the same on each side which i call "factoring the powers" as mathematical as that sounds..

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(Original post by

For these you need to make the base numbers equal eachother, so for example 2^2 = 4, so if you had 4^t+1 = 2^t you could do (2^2)^t+1 = 2^2t+2 = 2^t, therefore 2t+2 = t, t = -2. This can be applied to powers of 3 so 2^3 = 8.

For the later questions if x^2 = y then the square root of y is x and vice versa.

For the last one remember that the square root of x is x^0.5.

**fliscia**)For these you need to make the base numbers equal eachother, so for example 2^2 = 4, so if you had 4^t+1 = 2^t you could do (2^2)^t+1 = 2^2t+2 = 2^t, therefore 2t+2 = t, t = -2. This can be applied to powers of 3 so 2^3 = 8.

For the later questions if x^2 = y then the square root of y is x and vice versa.

For the last one remember that the square root of x is x^0.5.

^{5 }+ 7=100

I took away 7 and ended up with:

^{4r^5 =93 }

^{And Im not sure what to do next or even if Im approaching the question right, could you please give me a clue for this question? }

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#6

(Original post by

Can someone please tell me how to solve these questions,I have no idea what steps I should take,any help would be much appreciated.

7

9

4r

(4r to the power of 5 + 7 =100)

s

(s to the power of -5 is = to 4

simplify: (2√x)

———

8x

(2 root x to the power of 4 over 8x)

**Anonymous1502**)Can someone please tell me how to solve these questions,I have no idea what steps I should take,any help would be much appreciated.

7

^{t+6}=49^{2t}^{(7 to the power of t+6 is equal to 49 to power of 2t)}9

^{y+8 }= 27^{y+5}^{(9 to the power of y+8 is equal to 27 to the power of y+5)}4r

^{5 }+ 7=100(4r to the power of 5 + 7 =100)

s

^{-5}=4(s to the power of -5 is = to 4

simplify: (2√x)

^{4}———

8x

(2 root x to the power of 4 over 8x)

For both of these questions, simplify both sides to the same base i.e

For , move the unknowns to one side so

Now to remove the power, you flip the power to the other side i.e

So going back to the question, apply this to find the value of r.

For , now you must know that so use this method as well as the method I told you previously about flipping powers to the other side to find your value of s.

For , you must know that .

So you have ,

Then apply the power of 4 (i.e ) then simplify this using the denominator.

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#7

(Original post by

For this question: 4r

I took away 7 and ended up with:

**Anonymous1502**)For this question: 4r

^{5 }+ 7=100I took away 7 and ended up with:

^{4r^5 =93 }^{And Im not sure what to do next or even if Im approaching the question right, could you please give me a clue for this question? }Furthermore if r times itself 5 times is x, then what is r?

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(Original post by

If 4 of r^5 is 93, then what is r^5?

Furthermore if r times itself 5 times is x, then what is r?

**fliscia**)If 4 of r^5 is 93, then what is r^5?

Furthermore if r times itself 5 times is x, then what is r?

then 23.25= r^5 then I did to the power of 5 root 23.35 and got 1.88 to 3sf.

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#9

(Original post by

I solved it now,I took away the 7 and divided by 4 so I had 93/4 = r^5

then 23.25= r^5 then I did to the power of 5 root 23.35 and got 1.88 to 3sf.

**Anonymous1502**)I solved it now,I took away the 7 and divided by 4 so I had 93/4 = r^5

then 23.25= r^5 then I did to the power of 5 root 23.35 and got 1.88 to 3sf.

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(Original post by

For both of these questions, simplify both sides to the same base i.e

For , move the unknowns to one side so

Now to remove the power, you flip the power to the other side i.e

So going back to the question, apply this to find the value of r.

For , now you must know that so use this method as well as the method I told you previously about flipping powers to the other side to find your value of s.

For , you must know that .

So you have ,

Then apply the power of 4 (i.e ) then simplify this using the denominator.

**ManLike007**)For both of these questions, simplify both sides to the same base i.e

For , move the unknowns to one side so

Now to remove the power, you flip the power to the other side i.e

So going back to the question, apply this to find the value of r.

For , now you must know that so use this method as well as the method I told you previously about flipping powers to the other side to find your value of s.

For , you must know that .

So you have ,

Then apply the power of 4 (i.e ) then simplify this using the denominator.

(2√x)

^{4}

———

8x

Could you please tell me how you got 2 to the power of 1/2 to the power of 4?

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#11

(Original post by

Thank you for your help but Im still struggling to solve:

(2√x)

———

8x

Could you please tell me how you got 2 to the power of 1/2 to the power of 4?

**Anonymous1502**)Thank you for your help but Im still struggling to solve:

(2√x)

^{4}———

8x

Could you please tell me how you got 2 to the power of 1/2 to the power of 4?

**is the same as**.

The numerator now becomes because before you had but we need this in terms of powers to simplify this.

Now as I said is the same as

So to simplify the numerator,

Can you work from here?

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(Original post by

As I said, you need to know that

The numerator now becomes because before you had but we need this in terms of powers to simplify this.

Now as I said is the same as

So to simplify the numerator,

Can you work from here?

**ManLike007**)As I said, you need to know that

**is the same as**.The numerator now becomes because before you had but we need this in terms of powers to simplify this.

Now as I said is the same as

So to simplify the numerator,

Can you work from here?

16(x)^2over 8x

then I simplified to get only 2^2 which is 4 and then on my calculator i substituted the 4 for x and got 8 as my answer

is this correct?

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#13

(Original post by

so I did 2 to the power of 4 which is 16 and x ^1/2 times the power of 4 to get

16(x)^2over 8x

**Anonymous1502**)so I did 2 to the power of 4 which is 16 and x ^1/2 times the power of 4 to get

16(x)^2over 8x

(Original post by

then I simplified to get only 2^2 which is 4 and then on my calculator i substituted the 4 for x and got 8 as my answer

**Anonymous1502**)then I simplified to get only 2^2 which is 4 and then on my calculator i substituted the 4 for x and got 8 as my answer

Let me simplify this a bit more for you,

is the same as

Can you work from here?

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(Original post by

So you have which is correct.

I don't quite understand what you've done here because your answer should be in the form of where is an integer, I don't know what you've substituted in unless you haven't told the full question.

Let me simplify this a bit more for you,

is the same as

Can you work from here?

**ManLike007**)So you have which is correct.

I don't quite understand what you've done here because your answer should be in the form of where is an integer, I don't know what you've substituted in unless you haven't told the full question.

Let me simplify this a bit more for you,

is the same as

Can you work from here?

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#15

(Original post by

16/8 simplifies to 2. x^2/x simplifies to only x, so 2 * x =2x. So is 2x the correct answer or do I have to do another step?

**Anonymous1502**)16/8 simplifies to 2. x^2/x simplifies to only x, so 2 * x =2x. So is 2x the correct answer or do I have to do another step?

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(Original post by

Yes that's correct! The answer simplifies down to . You're just simplifying as your original post said.

**ManLike007**)Yes that's correct! The answer simplifies down to . You're just simplifying as your original post said.

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