Following the generalized form that you wrote, you know that a negative exponent sends its base to the denominator (or numerator if it's in the denominator already). Or to put it formally as you wrote it, for any nonzero real number a and natural number n, <span>the negative rule of exponents states that </span>
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So,
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Blue beads: 100/130, which reduces to 10/13.
Red beads: 20/130, which reduces to 2/13.
You're just taking the fraction of the certain color of beads compared with the total number of beads, which is 130.
She owes him $0.75 because if she paid him $1.50 already you just subtract that from $2.25
0.035x+0.045x=427.50
0.08x=427.50
x=427.50/0.08
x=5343.75
x+x+1500=5343.75
2x=5343.75-1500
2x=3843.75
x=1921.88 first
1921.88+1500=3421.88 second
The fourth one should be the correct answer