Algebra

23^9 × 23^7 = 23^[]

Step-by-step solution with explanation

Final Answer

, so

Step-by-step solution

1

Identify the bases being multiplied

Both terms have the same base, 23. When we multiply powers with the same base, we can use the Product of Powers rule.
2

Apply the Product of Powers rule

When multiplying two powers with the same base, keep the base and add the exponents together. This rule works for any base.
3

Add the exponents together

Simply add the two exponents: 9 plus 7 equals 16. The base 23 stays the same.
4

Write the final simplified expression

The missing exponent in the box is 16. There is exactly one solution to this problem.

Understanding this problem

Learning Insight

The Product of Powers rule works because exponents are just shorthand for repeated multiplication. means 23 multiplied by itself 9 times, and means 23 multiplied by itself 7 more times. Combining them gives 23 multiplied by itself times total.

Quick Tip

Same base multiplying? Just ADD the exponents. Think: 'multiply → add.' If you see division with the same base, you SUBTRACT instead.

Common Mistake

A common mistake is multiplying the exponents instead of adding them — writing instead of . Only multiply exponents when you have a power raised to another power, like .