Question

Apply the properties of integer exponents to generate equivalent expressions to (14^3x27^-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

you did a lot of math, but changed the original expression!
(14^3x27^-7)^0 / 3^4 = 1/3^4

Answer 2

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

(14^3 * 27^(-7))^(0/3^4)

First, let's simplify the exponents inside the parentheses:
14^3 = 14 * 14 * 14 = 2744
27^(-7) = 1/27^7

Now, rewrite the expression:
(2744 * (1/27^7))^(0/3^4)

Next, simplify the exponent (0/3^4):
0/3^4 = 0/81 = 0

Now, the expression becomes:
(2744 * (1/27^7))^0

Any number raised to the power of 0 is equal to 1. Therefore:
(2744 * (1/27^7))^0 = 1

Thus, the simplified expression is equal to 1.

Answer 3

Apologies for the confusion. Let's apply the properties of integer exponents to generate equivalent expressions for the original expression:

(14^3 * 27^(-7))^0 / 3^4

Using the property (a^m * b^n)^p = a^(m*p) * b^(n*p), we can simplify the expression inside the parentheses:

14^(3*0) * 27^(-7*0) = 14^0 * 27^0

Any nonzero number raised to the power of 0 is equal to 1. Therefore, we have:

1 * 1 = 1

Finally, we are left with:

1 / 3^4

Simplifying this expression, we have:

1 / 81

So, the simplified fraction without remaining exponents is 1/81.