33Answer:
120 [tex]\frac{29}{30}[/tex]
Step-by-step explanation:
Using the rules of exponents
• [tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^{m} }[/tex]
• [tex]a^{\frac{m}{n} }[/tex] ⇔[tex]\sqrt[n]{a^{m} }[/tex]
Evaluating each term
[tex]225^{-\frac{1}{2} }[/tex] = [tex]\frac{1}{225^{\frac{1}{2} } }[/tex] = [tex]\frac{1}{15}[/tex]
[tex]1000^{-\frac{1}{3} }[/tex] = [tex]\frac{1}{1000^{\frac{1}{3} } }[/tex] = [tex]\frac{1}{10}[/tex]
[tex]1331^{\frac{2}{3} }[/tex] = [tex]\sqrt[3]{1331^{2} }[/tex] = 121
Hence
[tex]\frac{1}{15}[/tex] - [tex]\frac{1}{10}[/tex] + 121
= 121 - [tex]\frac{1}{30}[/tex] = 20 [tex]\frac{29}{30}[/tex]
