81 x 27 / 3^2 can be simplyfied to 3^n find value of n

To simplify \( 81 \times 27 \div 3^2 \) and express it in terms of \( 3^n \), let's go through the steps:

1. **Rewrite 81 and 27 as powers of 3:**
   \[
   81 = 3^4 \quad \text{and} \quad 27 = 3^3
   \]

   So, we can substitute these values into the expression:
   \[
   81 \times 27 \div 3^2 = 3^4 \times 3^3 \div 3^2
   \]

2. **Combine the powers of 3 in the numerator:**
   \[
   3^4 \times 3^3 = 3^{4+3} = 3^7
   \]

   So now the expression becomes:
   \[
   3^7 \div 3^2
   \]

3. **Simplify using the rule for dividing powers (subtract exponents):**
   \[
   3^7 \div 3^2 = 3^{7-2} = 3^5
   \]

Thus, the expression simplifies to \( 3^5 \). Therefore, the value of \( n \) is:
\[
n = 5
\]

Would you like further details, or do you have any questions?

Here are 5 related questions to explore:

1. How would you simplify \( 27 \times 9 \div 3^3 \)?
2. If \( 81 = 3^4 \), what is \( 243 \) in terms of a power of 3?
3. What is the general rule for multiplying and dividing exponents with the same base?
4. How can we express \( 9 \times 3 \div 27 \) in terms of \( 3^n \)?
5. What would change if the expression had been \( 81 \times 27 \times 3^2 \)?

**Tip:** When simplifying expressions with exponents, always look for opportunities to rewrite numbers as powers of a common base for easier manipulation.

81 x 27 / 3^2 can be simplified to 3^n, find the value of n.

Learn how to simplify the expression 81 x 27 / 3^2 to a power of 3 and find the value of n. This step-by-step guide demonstrates the use of exponentiation rules to rewrite numbers as powers of 3 and simplify the expression. Suitable for students in Grades 7-9.

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