Question

Solve for 'p'

The equation is in the picture attached. Can you please explain the PROCESS? I know that the exponent of p = 0.5 but I don't know the process of finding it. I just guessed.

Thank you in advance

Answer 1

`\left((9a^(-4))/(25)\right)^p=\frac3{5a^2}`

`\left(\frac9{25a^4}\right)^p=\frac3{5a^2}`

One way to find
`p` is to notice that the part on the left hand side within the parentheses can be written as a square:


`\frac9{25a^4}=(3^2)/(5^2(a^2)^2)=\left(\frac3{5a^2}\right)^2`

So you could write


`\left(\left(\frac3{5a^2}\right)^2\right)^p=\left(\frac3{5a^2}\right)^(2p)=\frac3{5a^2}`

Since these two expressions are equal, and the bases are the same, you know the exponents must be equal, with the exponent on the right hand side being 1. So
`2p=1`, or
`p=\frac12`.