The Product Rule of Exponents states that when you multiply two expressions that have the same base, you add their exponents. The correct expressions that can be developed using this rule would be:
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\( 10^8 \times 10^8 \) can be simplified to \( 10^{8+8} = 10^{16} \).
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\( 32^7 \) does not follow the rule since it is just a single base raised to an exponent.
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\( (5^2)^9 \) can be simplified using the Power Rule instead, which states that you multiply the exponents, giving \( 5^{2 \times 9} = 5^{18} \).
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\( 6^2 \times 7^3 \) does not apply the Product Rule as they have different bases.
Therefore, the expression that correctly uses the Product Rule of Exponents is \( 10^8 \times 10^8 \).