Algebra

17^4 × 17 = 17^[]

Step-by-step solution with explanation

Final Answer

, so

Step-by-step solution

1

Identify the bases and exponents

We rewrite 17 as so every term clearly shows its exponent. This makes the rule easier to apply.
2

Apply the product of powers rule

When you multiply two numbers with the SAME base, you ADD the exponents. The base (17) stays the same.
3

Add the exponents together

Simple addition gives us the new exponent. So the missing box is filled with 5.
4

Write the final result

The completed equation shows that multiplying by equals .

Understanding this problem

Learning Insight

The product of powers rule works because exponents are just shorthand for repeated multiplication. means four 17s multiplied together times one more 17 — that is five 17s total, or . The base never changes; only the count of factors grows.

Quick Tip

Same base, multiplying? Just ADD the exponents. Think of exponents as a count of how many times the base appears as a factor.

Common Mistake

Students often MULTIPLY the exponents instead of adding them, writing instead of . Multiplying exponents is the rule for a POWER raised to another POWER, like — not for multiplication of two separate terms.