Select all the expressions that are equivalent to $5^{25}/5$ . $\newline$ Multi-select Choices: $\newline$ (A) $5^{24}$ $\newline$ (B) $1/5^{25}$ $\newline$ (C) $5^{25}$ $\newline$ (D) $5^{26}$

Full solution

Q. Select all the expressions that are equivalent to

5^{25}/5

\newline

Multi-select Choices:

\newline

(A)

5^{24}

\newline

(B)

1/5^{25}

\newline

(C)

5^{25}

\newline

(D)

5^{26}

Simplify Exponent Division: Simplify the expression $5^{25}/5$ . What operation should we perform with the exponents when dividing powers with the same base? When we divide powers with the same base, we subtract the exponents. $a^m / a^n = a^{(m - n)}$
Calculate Result: Calculate $5^{25}/5$ using the rule from Step $1$ . $\newline$ $5^{25} / 5^{1} = 5^{25 - 1} = 5^{24}$
Compare with Choices: Compare the result from Step $2$ with the given choices. $\newline$ $5^{24}$ matches choice (A), so (A) is equivalent to $\frac{5^{25}}{5}$ .
Check Choice (B): Check if choice (B) is equivalent to $5^{25}/5$ . $1/5^{25}$ is not equivalent to $5^{25}/5$ because $1/5^{25}$ is the reciprocal of $5^{25}$ , not a division by $5$ .
Check Choice (C): Check if choice (C) is equivalent to $5^{25}/5$ . $5^{25}$ is not equivalent to $5^{25}/5$ because no division by $5$ has been performed in choice (C).
Check Choice (D): Check if choice (D) is equivalent to $5^{25}/5$ . $\newline$ $5^{26}$ is not equivalent to $5^{25}/5$ because $5^{26}$ would result from multiplying $5^{25}$ by $5$ , not dividing by $5$ .