Which expression is equivalent to $5^-8*5^3$ ?

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Answer 1 · 2016-12-09T22:34:31

$5^-5$ or $1/5^5$ or $1/3125$

Using the rules for exponents ( $color(red)(x^a*x^b = x^(a+b))$ ):

$5^-8*5^3 -> 5^(-8+3) -> 5^-5$

We can convert further using another rule for exponents ( $color(red)(x^-a = 1/x^-a)$ ):

$5^-5 -> 1/5^5$

And then converting the exponent to a number gives:

$1/(5*5*5*5*5) -> 1/3125$

Which expression is equivalent to 5^-8*5^35^-8*5^3?