Question

Apply the Properties of Integer Exponents to generate equivalent expressions to (7^-3)^7 times 7^20/ 6-2

Answer 1

Provide it as an Improper fraction

Answer 2

To apply the properties of integer exponents, we will simplify each term separately.

First, let's simplify the term (7^-3)^7:

Using the property of exponentiation, we know that (a^m)^n = a^(m*n). Therefore, we have:
(7^-3)^7 = 7^(-3*7) = 7^-21

Next, let's simplify the term 7^20:

When we raise a number to a negative exponent, it is equivalent to taking the reciprocal of the number raised to the positive exponent. So, we have:
7^20 = 1/(7^-20)

Now, let's simplify the term 6^-2:

Using the property of exponentiation, we know that a^-n = 1/a^n. Therefore, we have:
6^-2 = 1/6^2 = 1/36

Now, let's substitute the simplified terms back into the original expression:

(7^-3)^7 * 7^20 / 6^-2

Substituting (7^-3)^7 = 7^-21, 7^20 = 1/(7^-20), and 6^-2 = 1/36:

= 7^-21 * (1/(7^-20)) / (1/36)

When dividing by a fraction, we can multiply by its reciprocal, so:

= 7^-21 * (1/(7^-20)) * (36/1)

Multiplying fractions, we multiply the numerators together and the denominators together:

= (7^-21 * 1 * 36) / (1 * 7^-20)

Using the property of exponentiation, we can rewrite the expression as:

= 36 / (7^(-21) * 7^20)

When we multiply with the same base, we add the exponents:

= 36 / 7^(-21 + 20)

= 36 / 7^-1

Using the property of exponentiation, we know that a^-n is equivalent to 1/a^n. Therefore:

= 36 * 7^1

= 36 * 7

= 252

Therefore, the equivalent expression to (7^-3)^7 * 7^20 / 6^-2 is 252.

Answer 3

The equivalent expression is 252, which can also be written as the improper fraction 252/1.