How do you simplify #((10s^0 )(6s^-5)) /((3s^-7)(10s^8))#?

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Answer 1 · 2016-09-26T23:38:42

#2/s^6#

#frac{(10s^0)(6s^-5)}{(3s^-7)(10s^8)}#

Anything with a negative exponent in the numerator can be moved to the denominator with a positive exponent (#x^-a = 1/x^a(10s^8}#)

And, anything with a negative exponent in the denominator can be moved to the numerator with a positive exponent (#1/x^-a=x^a#)

#frac{(10s^0)(6)s^7}{(3)(s^5)(10s^8)}#

Anything to the zero power equals one (#x^0=1#)

#frac{(10)(1)(6)s^7}{3(s^5)(10s^8)}#

Simplifyig the coefficients:
#frac{60s^7}{30s^5s^10}=frac{2s^7}{s^5s^8}#

When multiplying with the same base, add the exponents
(#x^a*x^b=x^(a+b)#)
#frac{2s^7}{s^13}#

When dividing with the same base, subtract the exponents.
(#x^a/x^b=x^(a-b)#)

#2s^-6 =2/s^6#