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9x^3/2 Times 8/x^8---- If you can explain this to me, and answer; it would be greatly appreciated. Thank you

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4 Answers

9 X ^3 / 2  * 8 / X^8
 
   ( 9 * 8 )/ 2  X^3/ X^8 =
 
     36  X ^3/ X^8 =
 
      36  X ^ 3/ X ^8 = 36 X ^ -5 = 36/ X ^ 5 
 
    Basically use laws of multiplication/ division of the  exponent with the same base, where for multiplication
 
      write one base , and add the exponent, and division subtract the exponents.
 
       a ^ m * a ^n = a ^ ( m+n)   ,/  negative exponents are reciprocal of base with positive exponents
 
 
       a ^m / a ^n = a ^ ( m- n)   / a ^ -m = 1/a^m      
9x3/2 * 8/x8 
 
When you multiply this out, you get:
 
(9x3/2)(8)          ------>     72x3/2
    x8                                            x8
 
You'll notice, both x's in the numerator and also in the denominator have exponents; so, this can be simplified.
When simplifying variable's exponents across a division bar, it follows certain rules:
[numerator's exponent] - [denominator's exponent]
 
x3/2 - x8  ------> 3/2 - 8  ------> 3/2 - 16/2
[I multiplied 8 by two so that both fractions had the same denominator]
 
------> x-exponent = -13/2
because the exponent is negative, the exponent is in the denominator
 
Final Answer ------> _72  
                               x13/2
Hi Abby;
[(9x3)/2](8/x8)
First....
x3/x8
Let's subtract exponentials.  This is...
3-8=-5
x-5 or 1/x5
(9/2)(8/x5)
Now, we will multiply numerators together...(9)(8)=72
And, we will multiply denominators together...(2)(x5)=2x5
72/(2x5)
72/2=36
36/xor 36x-5
(9x^3/2)(8/x^8)

= 9*8*(x^3/2)/(x^8) by commutative prop.

= 72 x^(3/2 - 8) by exponent rules

= 72 x^(3/2 - 16/2)

= 72 x^(-13/2)

= 72/x^(13/2) by exponent rules