Express in power notation -645/14641
Answers
Answer:
GIVEN :
The expression is \frac{-625}{14641}
14641
−625
TO FIND :
Express in power notation of the given expression
SOLUTION :
Given that the expression is \frac{-625}{14641}
14641
−625
Now solving the expression as below:
\frac{-625}{14641}
14641
−625
=-\frac{25^2}{121^2}=−
121
2
25
2
=-\frac{(5^2)^2}{(11^2)^2}=−
(11
2
)
2
(5
2
)
2
By using the Exponent power rule is given by :
(a^m)^n=a^{mn}(a
m
)
n
=a
mn
=-\frac{5^4}{11^4}=−
11
4
5
4
By using the Exponent property is given by :
\frac{a^m}{b^m}=(\frac{a}{b})^m
b
m
a
m
=(
b
a
)
m
=-(\frac{5}{11})^4=−(
11
5
)
4
∴ \frac{-625}{14641}=-(\frac{5}{11})^4
14641
−625
=−(
11
5
)
4
∴ the given expression in power notation is -(\frac{5}{11})^4−(
11
5
)
4
∴ The given expression in power notation is \frac{-625}{14641}=-(\frac{5}{11})^4
14641
−625
=−(
11
5
)
4