Question

Stuck on this please help

Answer 1

The answers are given below.

Explanation:

7. Simplified Fractions/Integers:

a.
`$ (25)^{(-3)/(2)} $`

=
`$ (5^2)^{(-3)/(2)} $`

=
`$ 5^(-3) $`

=
`$ (1)/(5^3) = (1)/(125) $` is the required answer.

b.
`$ \bigg ( (1)/(7) \bigg )^(2) $`

=
`$ \bigg( (1)/(7^2) \bigg) $`

=
`$ (1)/(49) $` is the required answer.

c.
`$ \bigg ( (1)/(7) \bigg) ^(-3) $`

=
`$ \bigg ( (1)/(7^(-3)) \bigg )$`

=
`$ 7^(3) $` = 343 is the required answer.

8. Simplified Fractions:

a.
`$ \bigg( (27)/(8) \bigg ) ^{(2)/(3)}$`

=
`$ \bigg ( (3^3)/(2^3) \bigg ) ^{(2)/(3)} $`

=
`$ \bigg ( (3)/(2) \bigg) ^2  $`

`$ = (9)/(4) $` is the required answer.

b.
`$ \bigg ( (4)/(25) \bigg)^{(-3)/(2)} $`

=
`$ \bigg ( (2^2)/(5^2) \bigg)^{(-3)/(2)}`

=
`$ \bigg ( (2^(-3))/(5^(-3)) \bigg ) $`

=
`$ \bigg( (5^3)/(2^3) \bigg ) $`

=
`$ (125)/(8) $` is the required answer.

9. Index Forms:

a. √3

=
`$ 3^{(1)/(2)} $` is the required answer.

b. ∛3

=
`$ 3^{(1)/(3)} $` is the required answer.

c.
`$\sqrt[6]{2} $`

=
`$ 2^{(1)/(6) $` is the required answer.

d.
`$ √(5^3) $`

=
`$ 5^{(3)/(2)} $` is the required answer.

e.
`$ \frac{1}{(\sqrt[3]{5})^2} $`

=
`$ \frac{1}{5^{(2)/(3)}} $`

=
`$ 5^{(-2)/(3)} $` is the required answer.