Apply the Properties of Integer Exponents to generate equivalent expressions to (14^3⋅27^−7)^0/34 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.
To apply the properties of integer exponents and generate equivalent expressions with only positive exponents, we can use the following rules:
1. For any non-zero number a, a^0 = 1.
2. For any number a, a^(-b) = 1/a^b.
Now let's apply these rules to simplify the expression:
(14^3⋅27^(-7))^0/34
First, let's simplify the exponents:
14^3 = 14 * 14 * 14
27^(-7) = 1/27^7
Now we can rewrite the expression as:
(14 * 14 * 14 * (1/27^7))^0/34
Next, let's simplify the expression inside the parentheses:
14 * 14 * 14 = 14^3
1/27^7 = (1^7)/(27^7) = 1/27^7
Now we have:
(14^3 * (1/27^7))^0/34
Next, let's simplify the expression inside the parentheses again:
14^3 * (1/27^7) = 14^3/27^7
Now we have:
(14^3/27^7)^0/34
Now we can simplify the entire expression to:
(1)^0/34
Since any number raised to the power of 0 is equal to 1 (except for 0^0, which is undefined), we have:
1/34
Therefore, the simplified fraction with no remaining exponents is 1/34.