Question

My 13 year old ask this question, and I didnt know where to start...

Answer 1

When multiplying exponents of the same base, add powers so something like y^(a)•y^(b) becomes:

y^(a+b)

Because the bases are the same (the base is y)

Powers in the denominator can be written in the numerator by changing the signs of the power so something like 1/y^(a) becomes:

y^(-a)

And finally, given the following equation:

y^a = y^(4), then a = 4

For this question, work with the right hand side, convert the radical to exponent form, use the multiplying exponent rule, re-write using negative exponents, then solve for m

Answer 2

is it -5/3?

1/p means p\^-1

the cube root p raised to square means 2/3 since its written in  divided by 1 form i suppose its -2/3

p\^-1 x p\^-2/3 as per the property of exponent when bases are same and you have to multiply you add the powers which gives us -5/3

so m=-5/3

Answer 3

Take logarithm of both sides.

Answer 4

I learned logs in Kumon at age 12 but learned it in class at 17 lol

Answer 5

This entire time I saw X as a variable, whoops x\^1  \* p\^2/3, you add them together - p\^5/3, so p\^m = 1/(p\^5/3), which is the same as( p\^-5/3)/1, which is the same as p\^-5/3, therefore m = -5/3

Answer 6

Alternatively, change P into any base it really doesn't matter, 1,2, 3, pi, Eulers constant, 69, it doesnt matter, then take the log of both sides, ill use 3 as an example, log(1/(3\*CubeRt(3)\^2) / log(3) = -5/3