Question

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

Answer 1

wrong yet again!

(14^3×27^-7)^0/3^4 = 1/3^4 = 1/81

Answer 2

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.

Answer 3

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.