Question

Given the algebraic expression 125x7^3) -1^3 create an equivalent expression.​

Answer 1

third option

Explanation:

using the rule of exponents

`(a^m)^(n)` =
`a^(mn)`

`a^(-m)` =
`(1)/(a^(m) )`

`a^{(m)/(n) }` =
`(\sqrt[n]{a})^m`

given

`(125x^{(7)/(3) }) ^{-(1)/(3) }`

=
`125^{-(1)/(3) }` ×
`x^{-(7)/(9) }`

=
`\frac{1}{125^{(1)/(3) } }` ×
`\frac{1}{x^{(7)/(9) } }`

=
`\frac{1}{\sqrt[3]{125} }` ×
`\frac{1}{x^{(7)/(9) } }`

=
`(1)/(5)` ×
`\frac{1}{x^{(7)/(9) } }`

=
`\frac{1}{5x^{(7)/(9) } }`