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

## 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

9x

^{3/2}* 8/x^{8}When you multiply this out, you get:

(9x

^{3/2})(8) ------> 72x^{3/2} x

^{8 }x^{8}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]

x

^{3/2}- x^{8}------> 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

x

^{13/2}Hi Abby;

[(9x

^{3})/2](8/x^{8})First....

x

^{3}/x^{8}Let's subtract exponentials. This is...

3-8=-5

x

^{-5}or 1/x^{5}(9/2)(8/x

^{5})Now, we will multiply numerators together...(9)(8)=72

And, we will multiply denominators together...(2)(x

^{5})=2x^{5}72/(2x

^{5})72/2=36

**36/x**

^{5 }or 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

= 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