What is the product of 10 to the 2 power and 10 to the 3 power?

To find the product of ( 10^2 ) and ( 10^3 ), you can use the property of exponents which states that when multiplying two powers with the same base, you add the exponents.

In this case, the base is 10. You have:

[ 10^2 \times 10^3 = 10^{2+3} ]

This simplifies to:

[ 10^5 ]

So, the product of ( 10^2 ) and ( 10^3 ) is ( 10^5 ). This demonstrates how the laws of exponents apply, confirming that adding the exponents gives the correct result. Therefore, ( 10^5 ) is the correct answer.