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Simplify the following and express each with positive exponent:
\( \left((-5)^{3}\right)^{\frac{2}{3}}+(3)^{5} \div 3^{3}+\left(\frac{1}{7}\right)^{0} \)
Given: $\left((-5)^{3}\right)^{\frac{2}{3}}+\frac{3^{5}}{3^{3}}+\left(\frac{1}{7}\right)^{0}$
To do: Simplify and express with positive exponent
Solution:
Apply rule $a^{0}=1$, a ≠ 0
$\left(\frac{1}{7}\right)^{0}=1$
$=\left((-5)^{3}\right)^{\frac{2}{3}}+\frac{3^{5}}{3^{3}}+1$
$\left((-5)^{3}\right)^{\frac{2}{3}}=(-5)^{2} = 5^2$
$\frac{3^{5}}{3^{3}}=3^{2}$
$=5^{2}+3^{2}+1$
$5^{2}=25$
$=25+3^{2}+1$
$3^{2}=9$
$=25+9+1$
Add the numbers:
$=35$
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