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: 

$=35$

Updated on: 10-Oct-2022

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