Apply the properties of integer exponents to generate equivalent expressions to (14^x27^-7)^0/3^4 with only positive exponents and solve the expression your answer will be a simplified fraction with no remaining exponents

Answer 1

To apply the properties of integer exponents, let's break down the given expression step by step:

(14^x27^-7)^(0/3^4)

First, let's simplify the exponents inside the parentheses using the multiplication property of exponents:
14^x * (1/27^7)^(0/3^4)

Next, let's simplify the exponents in the denominator of the fraction:
14^x * (1/3^(7*0)/(3^4*1))

The exponent in the numerator of the denominator becomes 0, so we can simplify further:
14^x * (1/3^0)/(3^4)

Any number (except 0) raised to the power of 0 equals 1, so:
14^x * (1/1)/(3^4)

1 divided by 1 is still 1, so we have:
14^x * 1/3^4

Finally, we can simplify the expression:
14^x/81

Therefore, the equivalent expression is 14^x/81.