Question

Which choice is equivalent to the expression below?

Answer 1

Answer: OPTION A

Step-by-step explanation:

We need to remember that Product of powers property, which states that:

$(a^m)(a^n)=a^{(m+n)}$

Let's check the options:

A. For $5^9*5^{\frac{9}{10}}*5^{\frac{6}{100}}*5^{\frac{9}{1000}}$ you can  apply the property mentioned before. Then:

$5^{(9+\frac{9}{10}+\frac{6}{100}+\frac{9}{1000})=5^{9.969}$

(It is the equivalent expression)

 B. Add the exponents:

 $5^9*5^{(\frac{9}{10}+\frac{9}{10}+\frac{6}{1000})=5^{10.806}$

(It is not the equivalent expression)

C. For $5^9*5^{\frac{96}{10}}*5^{\frac{9}{100}}}$ you can  apply the property mentioned before. Then:

 $5^{(9+\frac{96}{10}+\frac{9}{100})=5^{18.69}$

(It is not the equivalent expression)

D. We know that $5^{9.969}=9,290,347.808$ and we maje the addition indicated in this option, we get:

 $5^9+5^{\frac{9}{10}}+6^{\frac{6}{100}}=1,953,130.37$

(It is not the equivalent expression)

Answer 2

Answer: A, i just took this test