Simplify j · j · j^7 using positive exponents.
Understand the Problem
The question is asking to simplify the expression j · j · j^7 using the rules of exponents and to express the answer with positive exponents.
Answer
$$ j^9 $$
Answer for screen readers
$$ j^9 $$
Steps to Solve
-
Identify the expression to simplify
The expression to simplify is ( j \cdot j \cdot j^7 ). -
Combine the terms using exponent rules
According to the rules of exponents, when multiplying the same base, you add the exponents. Here, ( j = j^1 ) and can be expressed as: $$ j^1 \cdot j^1 \cdot j^7 $$ -
Add the exponents
Now, add the exponents together: $$ 1 + 1 + 7 = 9 $$ -
Write the simplified expression
The simplified expression, using positive exponents, is: $$ j^9 $$
$$ j^9 $$
More Information
The expression ( j \cdot j \cdot j^7 ) simplifies to ( j^9 ) by applying the exponent multiplication rule, which states that ( a^m \cdot a^n = a^{m+n} ).
Tips
- A common mistake is forgetting to convert the base without an exponent (like ( j )) to ( j^1 ).
- Another mistake is incorrectly adding the exponents.
AI-generated content may contain errors. Please verify critical information
