Question

What is the value of p?

Answer 1

`(x^(22))\cdot(x^7)^3`

when a number is power to a number a, and it is also power to another number b we can apply the property

`(x^a)^b=x^(a\cdot b)`

apply this to the expression above

`\begin{gathered} x^(22)\cdot(x^(7\cdot3)) \\ x^(22)\cdot x^(21) \end{gathered}`

continue by applying the property of a product between the same number as a base but with a different exponent

`x^a\cdot x^b=x^(a+b)`

apply this to the expression above

`\begin{gathered} x^(22)\cdot x^{21^{}} \\ x^(43) \end{gathered}`

the value of p is equal to 43.