Sure, let's break down each of the given fractions into power notation:
### (i) [tex]\(\frac{25}{36}\)[/tex]
First, identify the base numbers and their respective exponents:
- [tex]\(25 = 5^2\)[/tex]
- [tex]\(36 = 6^2\)[/tex]
Therefore,
[tex]\[
\frac{25}{36} = \frac{5^2}{6^2}
\][/tex]
### (ii) [tex]\(\frac{-27}{64}\)[/tex]
Next, we identify the base numbers and their respective exponents:
- [tex]\(-27 = (-3)^3\)[/tex]
- [tex]\(64 = 4^3\)[/tex]
Therefore,
[tex]\[
\frac{-27}{64} = \frac{(-3)^3}{4^3}
\][/tex]
### (iii) [tex]\(\frac{-32}{243}\)[/tex]
Again, we identify the base numbers and their respective exponents:
- [tex]\(-32 = (-2)^5\)[/tex]
- [tex]\(243 = 3^5\)[/tex]
Therefore,
[tex]\[
\frac{-32}{243} = \frac{(-2)^5}{3^5}
\][/tex]
### (iv) [tex]\(\frac{-1}{128}\)[/tex]
Finally, we identify the base numbers and their respective exponents:
- [tex]\(-1 = (-1)^7\)[/tex]
- [tex]\(128 = 2^7\)[/tex]
Therefore,
[tex]\[
\frac{-1}{128} = \frac{(-1)^7}{2^7}
\][/tex]
The power notations for the given fractions are:
(i) [tex]\(\frac{5^2}{6^2}\)[/tex]
(ii) [tex]\(\frac{(-3)^3}{4^3}\)[/tex]
(iii) [tex]\(\frac{(-2)^5}{3^5}\)[/tex]
(iv) [tex]\(\frac{(-1)^7}{2^7}\)[/tex]
To summarize:
- [tex]\(\frac{25}{36} = \frac{5^2}{6^2}\)[/tex]
- [tex]\(\frac{-27}{64} = \frac{(-3)^3}{4^3}\)[/tex]
- [tex]\(\frac{-32}{243} = \frac{(-2)^5}{3^5}\)[/tex]
- [tex]\(\frac{-1}{128} = \frac{(-1)^7}{2^7}\)[/tex]
These are the detailed steps to express each of the given fractions in power notation.
