Question

Which choice is equivalent to the expression below?

Answer 1

Answer: Choice C

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Explanation:

We can rewrite the exponent 9.969 as 9 + 0.9 + 0.06 + 0.009

Then convert each decimal to a fraction

• 0.9 = 9/10
• 0.06 = 6/100
• 0.009 = 9/1000

Your teacher is choosing not to reduce any of these fractions.

Then you'll use this rule $a^{b+c} = a^b*a^c$ to break up the exponent into the pieces mentioned.

So,

$5^{9.969} = 5^{9 + 0.9+0.06+0.009}\\\\5^{9.969} = 5^{9 + 9/10+6/100+9/1000}\\\\5^{9.969} = 5^{9}\cdot 5^{9/10}\cdot 5^{6/100}\cdot 5^{9/1000}$

Answer 2

It’s C I did it on a test