Answer:
[tex]\frac{25}{9}[/tex]
Step-by-step explanation:
To evaluate or simplify expressions with exponents, we use exponent rules.
1. An exponent is only a short cut for multiplication. It simplifies how we write the expression.
2. When we multiply terms with the same bases, we add exponents.
3. When we divide terms with the same bases, we subtract exponents.
4. When we have a base to the exponent of 0, it is 1.
5. A negative exponent creates a fraction.
6. When we raise an exponent to an exponent, we multiply exponents.
7. When we have exponents with parenthesis, we apply it to everything in the parenthesis.
We will use these rules to simplify. First we will substitute the values of a and k.
[tex](\frac{3^2a^{-2}}{3a^{-1}})^k =(\frac{3^25^{-2}}{3*5^{-1}})^{-2}=(\frac{3^25^1}{3*5^2})^{-2}=(\frac{3*5^2}{3^2*5^1})^{2}[/tex]
We simplified the negative exponents inside and outside the parenthesis. Remember a negative exponent switches its position in the numerator and denominator. We rewrote them with positive exponents.
Now apply the division rule for exponents for applying the exponent 2 outside the parenthesis.
[tex](\frac{3*5^2}{3^2*5^1})^{2}=(\frac{5}{3})^2[/tex]
Apply the exponent 2 and get [tex]\frac{25}{9}[/tex]
