Apply the Properties of Integer Exponents to generate equivalent expressions to (14 to the 3 power⋅27 to the −7 power) power of 0/ 3 to the 4th power with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)
To apply the properties of integer exponents, we can use the following rules:
1. Product rule: (a * b)^n = a^n * b^n
2. Power rule: (a^n)^m = a^(n*m)
3. Negative exponent rule: a^(-n) = 1/a^n
4. Zero exponent rule: a^0 = 1
First, let's simplify the expression using the properties of integer exponents:
(14^3 * 27^-7)^0 / (3^4)
Step 1: Simplify the expression within the parentheses using the product and negative exponent rules.
14^3 * (1/(27^7))^0 / (3^4)
14^3 * (1/27^7)^0 / (3^4)
14^3 * 1 / 3^4
Step 2: Simplify the exponent within the parentheses using the zero exponent rule.
14^3 * 1 / 3^4
Step 3: Simplify 14^3 and 3^4.
2744 * 1 / 81
Step 4: Simplify the fraction.
2744 / 81
So the simplified fraction is 2744/81.
that is not right
I apologize for the mistake. Let's go through the correct steps:
We are given the expression (14^3 * 27^-7)^0 / 3^4.
Step 1: Simplify the exponents using the properties of integer exponents.
(14^3 * (1/27^7))^0 / 3^4
(14^3 / 27^7)^0 / 3^4
Step 2: Apply the zero exponent rule.
1 / 3^4
Step 3: Simplify 3^4.
1 / 81
Therefore, the simplified expression is 1 / 81, which is a simplified fraction with no remaining exponents.