Apply the Properties of Integer Exponents to generate equivalent expressions to (7^-3)^7x7^20/6^-2
Using the properties of integer exponents, we can simplify the expression:
(7^-3)^7 * 7^20 / 6^-2
First, let's simplify the negative exponents:
(1/7^3)^7 * 7^20 / (1/6^2)
Next, let's simplify the exponents by multiplying:
(1/7^(3*7)) * 7^20 * (6^2/1)
Simplifying the exponent:
(1/7^21) * 7^20 * (6^2/1)
Using another property of exponents, we can combine the terms with the same base (7):
(1/7^21 * 7^20) * (6^2/1)
Simplifying the fraction:
(7^20/7^21) * (6^2/1)
Using the property of exponents again to subtract the exponents:
(1/7) * (6^2/1)
Simplifying the product:
6^2/7
Therefore, an equivalent expression to (7^-3)^7 * 7^20 / 6^-2 is 6^2/7.