To write the expression 100 × 1000 as a single power using the properties of exponents, we need to find a common base. Step 1: Express 100 and 1000 as powers of the same base.
Since both numbers are powers of 10, we can
rewrite them as: 100 = 10^2 1000 = 10^3 Step
2: Use the property of exponents that states
"when multiplying powers with the same base, add the exponents." In this case, we have:
10^2 × 10^3 Step 3: Apply the property by adding the exponents: 10^(2 + 3) Step 4:
Simplify the exponent: 10^5 So, the expression 100 × 1000 can be written as a single power:
10^5. This means that 100 × 1000 is equal to
10 raised to the power of 5.