The bulk section of a grocery store has two bins

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b2cutie456

25.04.2023

Mathematics

OPTION D.

Step-by-step explanation:

The missing options are:

$A. 5^3*5^{-5}\\B. 5^{-1}*5^{-1}\\C. 5^{-3}*5\\ D. 5^{-2}*5^4$

In order to solve this exercise it is necessary to remember the following:

1. The Product of powers property states that:

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

2. The Quotient of powers property states that:

$\frac{a^m}{a^n}=a^{(m-n)}$

3. The Negative exponent rule states the following:

$a^{-n}=\frac{1}{a^n}$

Then, knowing those properties you can check each option by applying them, in order to find which expression given in the exercise is equal to the fraction $\frac{1}{25}$ .

You get:

$A.\ 5^3*5^{-5}=5^{(3-5)}=5^{-2}=\frac{1}{5^2}=\frac{1}{25} \\\\B.\ 5^{-1}*5^{-1}=5^{(-1-1)}=5^{-2}=\frac{1}{5^2}=\frac{1}{25}\\\\C.\ 5^{-3}*5=5^{(-3+1)}=5^{-2}=\frac{1}{5^2}=\frac{1}{25}\\\\ D.\ 5^{-2}*5^4=5^{(-2+4)}=5^2=25$

Therefore, you can identify that the expression given in the OPTION D is not equal to $\frac{1}{25}$ .

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