To simplify the expression 37β 3β9 with positive exponents, we can use the following exponent rules:
1. Product of powers rule: am * an = am+n
2. Power of a power rule: (am)n = am*n
3. Negative exponent rule: a^-n = 1/an
Let's simplify the expression step by step:
37β
3β9
First, let's apply the negative exponent rule to get rid of the negative exponent:
37β
3β9 = 37 * 1/3^9
Next, let's simplify the fraction by applying the power of a power rule:
37 * 1/3^9 = 37 * 1/(3^3)^3
Now, let's apply the power of a power rule:
37 * 1/(3^3)^3 = 37 * 1/3^27
Finally, let's simplify the expression:
37 * 1/3^27 = 37/3^27
So, the simplified expression is 37/3^27.