Which two expressions are equivalent to each other?
9^-5
9^9/9^4
(9^2)^-3
9^4 · 9^-9
Which two expressions are equivalent to each other? 9^-5 9^9/9^4 (9^2)^-3 9^4 · 9^-9
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To find the equivalent expressions, we can simplify each one using the rules of exponents.
1. 9^-5: This is already simplified.
2. 9^9 / 9^4: Using the rule ( a^m / a^n = a^{m-n} ):
[
9^{9-4} = 9^5
]
3. (9^2)^-3: Using the power of a power rule ( (a^m)^n = a^{m cdot n} ):
[
9^{2 cdot -3} = 9^{-6}
]
4. 9^4 · 9^-9: Using the rule ( a^m cdot a^n = a^{m+n} ):
[
9^{4 + (-9)} = 9^{-5}
]
Now, to summarize:
– 9^-5 is equivalent to 9^{-5}.
– 9^9 / 9^4 simplifies to 9^5.
– (9^2)^-3 simplifies to 9^{-6}.
– 9^4 · 9^-9 simplifies to 9^{-5}.
The equivalent expressions are 9^-5 and 9^4 · 9^-9.