Express the following fraction in simplest form using only positive exponents.

Question

start fraction, 3, left parenthesis, s, cubed, right parenthesis, to the power 4 , divided by, 12, s, to the power 8 , end fraction
12s
8

3(s
3
)
4

​

Answer 1

To simplify the fraction \(\frac{3(s^3)^4}{12s^8}\), we can follow these steps:

1. Simplify the numerator: \[ (s^3)^4 = s^{3 \times 4} = s^{12} \] So the numerator becomes: \[ 3s^{12} \]

2. Rewrite the fraction: \[ \frac{3s^{12}}{12s^8} \]

3. Divide the coefficients: \[ \frac{3}{12} = \frac{1}{4} \]

4. Simplify the terms with the same base (using the rule \(\frac{a^m}{a^n} = a^{m-n}\)): \[ \frac{s^{12}}{s^8} = s^{12-8} = s^4 \]

5. Combine the results: \[ \frac{3s^{12}}{12s^8} = \frac{1}{4} s^4 \]

Thus, the simplified form of the fraction \(\frac{3(s^3)^4}{12s^8}\) is: \[ \frac{1}{4}s^4 \] or simply: \[ \frac{s^4}{4} \]

This represents the expression in simplest form using only positive exponents.