Answer: OPTION A
Step-by-step explanation:
We need to remember that Product of powers property, which states that:
[tex](a^m)(a^n)=a^{(m+n)}[/tex]
Let's check the options:
A. For [tex]5^9*5^{\frac{9}{10}}*5^{\frac{6}{100}}*5^{\frac{9}{1000}}[/tex] you can apply the property mentioned before. Then:
[tex]5^{(9+\frac{9}{10}+\frac{6}{100}+\frac{9}{1000})=5^{9.969}[/tex]
(It is the equivalent expression)
B. Add the exponents:
[tex]5^9*5^{(\frac{9}{10}+\frac{9}{10}+\frac{6}{1000})=5^{10.806}[/tex]
(It is not the equivalent expression)
C. For [tex]5^9*5^{\frac{96}{10}}*5^{\frac{9}{100}}}[/tex] you can apply the property mentioned before. Then:
[tex]5^{(9+\frac{96}{10}+\frac{9}{100})=5^{18.69}[/tex]
(It is not the equivalent expression)
D. We know that [tex]5^{9.969}=9,290,347.808[/tex] and we maje the addition indicated in this option, we get:
[tex]5^9+5^{\frac{9}{10}}+6^{\frac{6}{100}}=1,953,130.37[/tex]
(It is not the equivalent expression)
