Evaluate the decimal expression with powers of ten. Compute the value of 3 × 10^1 + 7 × 10^0 and select the correct result.

Introduction / Context:Powers of ten form the backbone of positional decimal notation. Expressions like a10^1 + b10^0 reconstruct numbers from digit weights, reinforcing how place value works.

Given Data / Assumptions:

• Evaluate: 3 * 10^1 + 7 * 10^0
• 10^1 = 10; 10^0 = 1

Concept / Approach:Use the definition of decimal place values. The tens place weight is 10^1; the ones place weight is 10^0. Multiply each coefficient by its positional weight and sum the results.

Step-by-Step Solution:

Verification / Alternative check:Recognize that 3 tens and 7 ones directly form the number 37 by positional notation rules.

Why Other Options Are Wrong:

• 3.7: misplaces the decimal point.
• 10: ignores the 7 * 1 term.
• 370: multiplies by an extra factor of 10.
• 307: misapplies place value as hundreds + ones.

Common Pitfalls:

• Mistaking 10^0 for 0 or forgetting that any nonzero number to the power 0 equals 1.

Final Answer:37