apply the properties of integer exponents to generate equivalent expression to (7 to the power of -3) to the power of 7 times 7 to the power of 20 divided by 6 to the power of -2

Answer 1

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

1. Start with (7^-3)^7:
According to the property (a^m)^n = a^(m*n), we can multiply the exponents:
(7^-3)^7 = 7^(-3*7) = 7^-21.

2. Then, multiply by 7^20:
According to the property a^m * a^n = a^(m+n), we can add the exponents:
7^-21 * 7^20 = 7^(-21 + 20) = 7^-1.

3. Lastly, divide by 6^-2:
According to the property a^m / a^n = a^(m-n), we can subtract the exponents:
7^-1 / 6^-2 = 7^-1 * 6^2 = 7^-1 * 36.

Therefore, the equivalent expression would be 7^-1 * 36.