Apply the Properties of Integer Exponents

Question

to generate equivalent expressions 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

To apply the properties of integer exponents to generate equivalent expressions with only positive exponents, we can simplify the given expression step by step:

Step 1: Rewrite the expression using the property a^n / b^n = (a/b)^n.
[(14^3)/(27^-7)]^(0/3^4)

Step 2: Apply the property (a^m)^n = a^(m*n) to the numerator.
[(14^(3*1))/(27^(-7*1))]^(0/3^4)

Step 3: Simplify the exponents in the numerator and denominator.
(14^3 / 27^-7)^(0/3^4)

Step 4: Apply the property (a^-n) = (1/a^n) to move the negative exponent in the denominator.
(14^3 / (1/27^7))^(0/3^4)

Step 5: Simplify the expression in the denominator.
(14^3 / 27^7)^(0/3^4)

Step 6: Apply the property a^0 = 1 to eliminate the exponent of zero.
1

Therefore, the equivalent expression with only positive exponents simplifies to 1.

So, the solution to the expression is 1.

Answer 2

wrong

Answer 3

Apologies for the mistake. Let's try again:

To apply the properties of integer exponents and generate equivalent expressions with only positive exponents, we can simplify the given expression step by step:

Step 1: Simplify the exponents in the numerator and denominator.
(14^3 - 27^(-7))^(0/3^4)

Step 2: Solve the powers with negative exponents by applying the property a^(-n) = 1/a^n.
(14^3 - 1/27^7)^(0/3^4)

Step 3: Apply the property a^0 = 1 to eliminate the exponent of zero.
(14^3 - 1/27^7)^0

Step 4: Any expression raised to the power of zero simplifies to 1.
1

Therefore, the equivalent expression with only positive exponents simplifies to 1.

So, the solution to the expression is 1.