Simplify: 26 * 26^8
The Correct Answer and Explanation is:
To simplify the expression 26×26826 \times 26^826×268, we can use the law of exponents. Specifically, the rule states: am×an=am+na^m \times a^n = a^{m+n}am×an=am+n
In this case, we have: 26×26826 \times 26^826×268
The number 26 is the same base as 26826^8268, so we can apply the exponent rule: 261×268=261+8=26926^1 \times 26^8 = 26^{1+8} = 26^9261×268=261+8=269
Thus, the simplified expression is: 26926^9269
Explanation:
- Step 1: Recognizing the same base: Both 26 and 26826^8268 share the same base (26), so we can apply the exponent rule for multiplying powers of the same base.
- Step 2: Adding the exponents: Using the rule am×an=am+na^m \times a^n = a^{m+n}am×an=am+n, we add the exponents 1 and 8 to get 9.
- Step 3: The result: The simplified expression is 26926^9269.
If you were to evaluate 26926^9269, you would calculate 262626 raised to the 9th power, which would give a much larger number. However, unless specified, the final simplified form is usually left as 26926^9269 unless numerical evaluation is requested.
