Algebra

11^12 × 11^3 = 11^x

Step-by-step solution with explanation

Final Answer

Step-by-step solution

1

Identify the bases on both sides

All three terms have the same base of 11. When bases match, we can work directly with the exponents.
2

Apply the product of powers rule

The product of powers rule says: when you multiply same bases, add the exponents. So .
3

Add the exponents together

Simply add 12 + 3 to get 15. Now the left side is .
4

Set the exponents equal and solve

Since both sides have the same base (11) and the equation is true, the exponents must be equal. So .

Understanding this problem

Learning Insight

The product of powers rule works because exponents are just shorthand for repeated multiplication. means 11 multiplied 12 times, and means 11 multiplied 3 more times — so together you have 11 multiplied 15 times, which is .

Quick Tip

Same base on both sides of a multiplication? Just add the exponents. Always check that the bases truly match before using this rule.

Common Mistake

Students often multiply the exponents instead of adding them — writing instead of . Multiplying exponents is the rule for a POWER raised to a POWER, like .