Which shows 
36
8
 decomposed into a product of powers?

To decompose \( \frac{36}{8} \) into a product of powers, we need to break down the numerator and the denominator into their prime factors:

- \( 36 = 2^2 \times 3^2 \)
- \( 8 = 2^3 \)

Now, represent \( \frac{36}{8} \) using these prime factorizations:

\[
\frac{36}{8} = \frac{2^2 \times 3^2}{2^3}
\]

Next, simplify by applying the quotient rule of exponents (\( \frac{a^m}{a^n} = a^{m-n} \)):

\[
\frac{36}{8} = 2^{2-3} \times 3^2 = 2^{-1} \times 3^2
\]

Thus, \( \frac{36}{8} \) decomposed into a product of powers is:

\[
2^{-1} \times 3^2
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you simplify fractions using prime factorizations?
2. What is the quotient rule for exponents?
3. How do you interpret negative exponents?
4. What are the steps for factoring a number into primes?
5. How would this decomposition change if we used different bases?

**Tip:** When simplifying expressions with exponents, always apply the exponent rules carefully to avoid mistakes!

Which shows 36/8 decomposed into a product of powers?

Explore how to decompose 36/8 into a product of powers by breaking it down into prime factors. Learn the quotient rule for exponents and how to simplify fractions using prime factorization. Suitable for students in Grades 6-8.

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