Select all the expressions that are equivalent to 10^3 * 6^3.
60^3
60^6 / 60^3
60^9
60^6
Select all the expressions that are equivalent to
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Select all the expressions that are equivalent to 10^3 * 6^3.
60^3
60^6 / 60^3
60^9
60^6
To determine which expressions are equivalent to (10^3 * 6^3), we can simplify the original expression first:
[
10^3 * 6^3 = (10 * 6)^3 = 60^3
]
Now, let’s analyze the options:
1. (60^3): This is equivalent, as shown above.
2. (60^6 / 60^3): This simplifies to (60^{6-3} = 60^3), which is equivalent.
3. (60^9): This is not equivalent, since (60^9) is greater than (60^3).
4. (60^6): This is also not equivalent, as it does not reduce to (60^3).
Thus, the correct equivalent expressions are (60^3) and (60^6 / 60^3).
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