Question

Apply the Properties of Integer Exponents to generate equivalent expressions to (7^-3)^7x7^20/6^-2 ⋅ with only positive exponents, then solve the expression.

Answer 1

To simplify the given expression and apply the properties of integer exponents, we start by multiplying the exponents within the parentheses:

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

Next, we multiply the exponents for 7^(-21) and 7^20:

7^(-21) ⋅ 7^20 = 7^(-21 + 20) = 7^(-1)

Now, let's simplify the other part of the expression:

6^-2 = 1/6^2 = 1/36

Finally, we can put the simplified expression together:

(7^-3)^7 ⋅ 7^20 / 6^-2 = 7^(-1) ⋅ 7^20 / 1/36 = 7^(-1) ⋅ 7^20 ⋅ 36

Using the property of multiplying exponents with the same base, we can add the exponents:

7^(-1) ⋅ 7^20 = 7^(20-1) = 7^19

Now, our expression becomes:

7^19 ⋅ 36

To solve this expression, we need to know the value of 7^19. Since it's a very large number, it's more practical to use a calculator or computer program to find the result.