Question

Question #9e52a

Answer 1

The product rule and the power rules in question are

• `a^mxxa^n = a^(m+n)`

• `a^m-:a^n = a^(m-n)`

• `(a^m)^n = a^(mxxn)`

(Note that the second rule comes directly from the first, because `1/a^x = a^(-x)`, so `a^m/a^n = a^mxxa^(-n) = a^(m+(-n)) = a^(m-n)`)

Rather than simply post answers to all of the questions on the worksheet, here are a couple of examples of each. These should show how to do the rest, as the problems are all effectively the same, save for the changed values.

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First set:

1) `5^(-8)xx5^(-5) = 5^(-8+(-5)) = 5^(-13)`

2) `18^(-4)xx18^(3) = 18^(-4+3)=18^(-1)`

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Second set:

1) `4^2-:4^10 = 4^(2-10) = 4^(-8)`

2) `19^7 -: 19^(-8) = 19^(7-(-8)) = 19^15`

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Third set:

1)`(15^9)^(-7) = 15^(9xx-7)=15^(-63)`

2)`(7^3)^6 = 7^(3xx6)=7^18`