Question

Which of the following properties are used when rewriting the expression 2a^-2+(2a^-2)^4

Answer 1

To rewrite the expression 2a^-2+(2a^-2)^4, we need to apply the properties of exponents:

1) The power of a power rule: (a^m)^n = a^(m*n)
2) The power of a product rule: (ab)^n = a^n * b^n
3) The power of a quotient rule: (a/b)^n = a^n / b^n

Let's simplify the expression step by step.

First, we have 2a^-2. To simplify this, we can use the power of a quotient rule. Since a^-2 can be written as 1/a^2, we have:

2a^-2 = 2 * (1/a^2) = 2/a^2

Now let's simplify (2a^-2)^4. Using the power of a power rule, we have:

(2/a^2)^4 = 2^4 / (a^2)^4 = 16 / a^8

Finally, we can rewrite the expression by plugging in the simplified forms:

2a^-2 + (2a^-2)^4 = 2/a^2 + 16/a^8