Question

If (8^9)^p=8^18what is the value of p

Answer 1

`\huge\boxed{p=2}`

Explanation:

In order to simplify this equation
`(8^9)^p = 8^(18)`, we have to use basic exponent rules.

Exponent rules tell us that
`(a^b)^c = a^(b\cdot c)`.

We have
`(8^9)^p`, so this means that it's equivalent to
`8^(9 \cdot p)` or just
`8^(9p)`.

Now, we have
`8^(9p)=8^(18)`

Let's just focus on the exponents for now.

Since we know that in order for
`8^(9p)` to be equivalent to
`8^(18)`, the exponents must be the exact same. So,
`9p=18`.

We can find p by divide both sides by 9.

`p = 2`

Hope this helped!