To find an expanded equivalent expression for \(5^{10}\), we will use the properties of exponents, specifically understanding how exponentiation works.
The expression \(5^{10}\) means that the base (5) is multiplied by itself 10 times. Thus, it can be expressed as:
\[ 5^{10} = 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \]
Now, let's analyze the provided options to identify which is an equivalent expanded form.
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(5⋅5)8: This means \( (5 \cdot 5)^8 \). By the Power Rule, \( (5^2)^8 = 5^{16} \). This does not equal \(5^{10}\).
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(5⋅5⋅5⋅5⋅5)⋅(5⋅5⋅5⋅5⋅5)⋅(5⋅5⋅5⋅5⋅5)⋅(5⋅5⋅5⋅5⋅5)⋅(5⋅5⋅5⋅5⋅5): This is multiplying five groups of five terms, each having five \(5\)s, which results in \(5^{25}\) (since \(5 \times 5 = 5^2\), and \(5^2 \times 5^2 \times 5^2 \times 5^2 \times 5^2 = 5^{10}\)). Thus, this is too high.
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(516)6: This means \((5^{16})^6\). Using the power of a power property, this simplifies to \(5^{96}\), which is also too high.
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(5⋅5)⋅(5⋅5)⋅(5⋅5)⋅(5⋅5)⋅(5⋅5): This means multiplying together five groups of \( (5 \cdot 5) \). Each \( (5 \cdot 5) = 5^2\), and therefore:
\[ (5 \cdot 5)^{5} = (5^2)^{5} = 5^{10} \]
This matches our original term \(5^{10}\).
So, the correct answer is:
\[ \text{(5⋅5)⋅(5⋅5)⋅(5⋅5)⋅(5⋅5)⋅(5⋅5)} \]