Question

Simplify using the laws of exponents. Use the box to the right of the variable as it’s simplified exponent.

Answer 1

Answer:
`3375m^(24)`Step-by-step explanation:

Given:

`(15m^8)\placeholder{⬚}^3`

To find:

to simplify using laws of exponents

First, we need to expand the expression:

`\begin{gathered} In\text{ exponent laws, a}^3\text{ = a }*\text{ a }*\text{ }a \\ \\ Applying\text{ same rule:} \\ (15m^8)\placeholder{⬚}^3\text{ = \lparen15m}^8)*(15m^8)\text{ }*(15m^8) \\ =\text{ 15 }*\text{ }m^8*\text{15 }*\text{ }m^8*\text{15 }*\text{ }m^8\text{ } \\ \\ collect\text{ like terms:} \\ =\text{ 15 }*\text{ 15 }*15\text{ }* m^8*\text{ }m^8*\text{ }m^8\text{ } \end{gathered}`
`\begin{gathered} Simpify: \\ 15*15*15\text{ = 3375} \\ \\ m^8\text{ }*\text{ m}^8\text{ }*\text{ m}^8 \\ when\text{ multiplying exponents with same base, } \\ \text{we will pick one of the base and add the exponents together } \\ m^8\text{ }*\text{ m}^8\text{ }*\text{ m}^8\text{ = m}^(8+8+8) \\ =\text{ m}^(24) \end{gathered}`
`\begin{gathered} 15*15*15* m^8* m^8* m^8\text{ = 3375 }*\text{ m}^(24) \\ \\ =\text{ 3375m}^(24) \end{gathered}`