Question

Create three expressions that are equivalent to 49x^8. At least one expression should use division and another should use multiplication. At least one needs to include a term with a negative exponent. Show how you know that your expressions are equivalent to 49x^8.

a. 7x^4 * 7x^4, (7x^4)^2, (7x^4)^2 / (7x^-4)
b. (7x^4)^2, 7x^4 * 7x^4, (7x^-4)^2
c. (7x^4)^2, 7x^4 * 7x^4, (7x^4)^-2
d. (7x^4)^2, 7x^-4 * 7x^-4, (7x^4)^-2

Answer 1

Three equivalent expressions to 49x^8 are provided, with step-by-step simplifications shown.

Step-by-step explanation:

Three expressions equivalent to 49x^8 are:

1. Expression 1: 7x^4 * 7x^4
2. Expression 2: (7x^4)^2
3. Expression 3: (7x^4)^2 / (7x^-4)

To show that these expressions are equivalent to 49x^8, we can simplify each expression:

1. Expression 1: 7x^4 * 7x^4 = 49x^8
2. Expression 2: (7x^4)^2 = 49x^8
3. Expression 3: (7x^4)^2 / (7x^-4) = 49x^8