Use the Properties of Integer Exponents to generate equivalent expressions with only positive exponents. Your answer will be simplified fraction. (14^3 * 27^-7)^0/3^4

Answer 1

Using the properties of integer exponents, we can simplify the expression as follows:

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

Since any number raised to the power of zero is equal to 1, we have:

(14^3 * 27^-7)^0 = 1/1

Next, we simplify the expression with positive exponents:

14^3 = (2^1 * 7^1)^3 = 2^3 * 7^3 = 8 * 343 = 2744

27^-7 = (3^3)^-7 = 3^-21

Therefore, the simplified expression is:

(14^3 * 27^-7)^0/3^4 = (2744 * 3^-21) / 81

To further simplify the expression, we can multiply the numerator and denominator by 3^21 and combine like terms:

(2744 * 3^-21) / 81 = 2744 / (81 * 3^21) = 2744 / 3^21 * 81

The simplified fraction is 2744 / (3^21 * 81).

Answer 2

thank you!

Answer 3

You're welcome! If you have any more questions, feel free to ask.