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Because:

  • that is how indices are defined, and
  • if they did not always work, they would not be called laws.
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Q: Why do the 5 laws of indices always work?
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How do you work out 8x2-5 equals?

you use BIDMAS Brackets Indices (Division Multiplication) (Addition Subtraction) the brackets always come first then Indices (to the power of) them multiply and divine have the same equality either and adding and subtracting are the same. so you would multiply 8x2=16 then you subtract 5 16-5=11.


What are the 5 laws of exponent?

Exponents are the same as powers or indices and so:- When multiplying terms add the indices: y2*y6 = y8 When dividing terms subtract the indices: x6/x2 = x4 Powers of powers multiply the the indices: (p2)3 = p6 Square root of: d8 = d8/2 = d4 Cube root of: p15 = p15/3 = p5 Remember:- Anything to the power of 0 is 1: x0 = 1 Anything to the power of 1 is just itself: x1 = x 1 raised to any power is just 1: 110 = 1


What is the product of prime factors for 370 using indices?

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What is 70 as a product of prime numbers in index form?

It is: 2*5*7 = 70 and no indices are needed


Express 60 as a product of prime factors uuing indices?

22 x 3 x 5


What does it mean to write your answers as powers?

It means to write out your answers in index or indices format as for example 5*5 = 25 which is the same as 52


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Write 90 as a product of prime factors in index form?

It is: 2 times 3^2 times 5 = 90 no indices are needed for 2 and 5


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No indices are needed because as a product of its prime factors: 3*5*7 = 105


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How do you solve X plus five to the one fifth minus x plus five to the sixth fifth?

This is relatively easy to solve, only requires application of the laws of indices. (x+5)1/5 - (x+5)6/5 = 0 => (x+5)1/5 - (x+5)(x+5)1/5 = 0 => (x+5)1/5 (1 - (x+5)) = 0 => -(x+5)1/5 (x+4)=0 since the expression equals 0 one term or the other has to be 0 therefore x= -4 or x= -5