Apply the property of integer exponents to generate equivalent expression to (14^3×27^-7)^0/3^4 with only positive exponents then solve the expression. Your answer will be a simplified fraction with no remaining exponents
wrong yet again!
(14^3×27^-7)^0/3^4 = 1/3^4 = 1/81
Apologies for the mistake in my previous response. Let's correctly apply the property of integer exponents to generate an equivalent expression with only positive exponents.
Using the property (a^m)^n = a^(m*n), we can simplify the expression as follows:
(14^3 × 27^-7)^(0/3^4)
= (14^3 × (1/27^7))^(0/3^4)
= (14^3 × 1/27^(7*0))^(0/3^4)
= (14^3 × 1/27^0)^(0/3^4)
Since any non-zero number raised to the power of zero is equal to 1, we have:
= (14^3 × 1/1)^(0/3^4)
= 14^3 × 1^(0/3^4)
= 14^3 × 1^0
= 14^3 × 1
= 14^3
Now, let's solve the expression 14^3:
14^3 = 14 × 14 × 14 = 2,744
Therefore, the simplified value of the expression (14^3×27^-7)^0/3^4 is 1/81.
To generate an equivalent expression with only positive exponents, we can apply the property of integer exponents:
Property of integer exponents: For any non-zero integer a and positive integers m and n, (a^m)^n = a^(m * n).
Let's simplify the given expression step by step:
Expression: (14^3 × 27^(-7))^(0/3^4)
Step 1: Simplify the exponents inside the parentheses using the property of integer exponents.
(14^3 × 27^(-7))^(0/3^4) = 14^(3 * (0/3^4)) × 27^(-7 * (0/3^4))
Since any number raised to the power of 0 is equal to 1, we have:
14^(3 * (0/3^4)) = 14^0
27^(-7 * (0/3^4)) = 27^0
Step 2: Simplify further by applying the property that any number (except 0) raised to the power of 0 is equal to 1.
14^0 = 1
27^0 = 1
The given expression simplifies to:
1 × 1 = 1
So, the simplified expression is 1.
Therefore, the answer is 1, which can be represented as the simplified fraction 1/1 or just 1.
To apply the property of integer exponents, we will first rewrite the expression in terms of positive exponents. Remember that a negative exponent can be rewritten as the reciprocal of the base raised to the positive exponent.
(14^3 × 27^-7)^(0/3^4)
= (14^3 × 1/27^7)^(0/81)
= (14^3/27^7)^(0/81)
Since any non-zero number raised to the power of zero is equal to 1, we can simplify the expression further:
= 1
Therefore, the value of the expression is 1.