(14^3⋅27^−7)^0/3^4 3^4 over the whole equation with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point
Let's start by simplifying the exponents in the expression.
First, we'll simplify the exponents inside the parentheses:
14^3 = (2^1*7^1)^3 = 2^3*7^3 = 8*343 = 2744
27^-7 = (3^3)^-7 = 3^-21
So, the expression becomes:
(2744*3^-21)^(0/3^4)
Next, we simplify the exponent of 0/3^4:
0/3^4 = 0/81 = 0
So, the expression simplifies further to:
(2744*3^-21)^0
Any number (except 0) raised to the power of 0 is equal to 1. So, the expression becomes:
1
Therefore, the simplified fraction with no remaining exponents is 1/1, which is just 1.
(14^3⋅27^−7)^0/3^4 3^4
anything^0 is one
( 1/3^4) * 3^4
= 1
You are correct, any number (except 0) raised to the power of 0 is equal to 1, so we have:
(14^3⋅27^−7)^0/3^4 3^4
= 1/3^4 * 3^4
= 1.