Select all the expressions that are equivalent to $5 \times 5^{-1}$ . $\newline$ Multi-select Choices: $\newline$ (A) $\frac{1}{5^0}$ $\newline$ (B) $5^{-1}$ $\newline$ (C) $1$ $\newline$ (D) $\frac{1}{5^{-1}}$

Full solution

Q. Select all the expressions that are equivalent to

5 \times 5^{-1}

\newline

Multi-select Choices:

\newline

(A)

\frac{1}{5^0}

\newline

(B)

5^{-1}

\newline

(C)

1

\newline

(D)

\frac{1}{5^{-1}}

Understand Expression: Understand the given expression $5 \times 5^{-1}$ . We need to simplify the expression $5 \times 5^{-1}$ using the property of exponents that states $a^m \times a^n = a^{(m+n)}$ .
Simplify Expression: Simplify the given expression. $\newline$ $5 \times 5^{-1} = 5^{1 + (-1)} = 5^0$ $\newline$ According to the exponent rules, any non-zero number raised to the power of $0$ is $1$ . $\newline$ So, $5^0 = 1$
Evaluate Choices: Evaluate the choices given. $\newline$ (A) $\frac{1}{5^0} = \frac{1}{1} = 1$ , which is equivalent to $5 \times 5^{-1}$ . $\newline$ (B) $5^{-1}$ is not equivalent to $5 \times 5^{-1}$ because $5^{-1}$ alone is $\frac{1}{5}$ , not $1$ . $\newline$ (C) $1$ is equivalent to $5 \times 5^{-1}$ , as we have already simplified it to $1$ . $\newline$ (D) $5 \times 5^{-1}$ $0$ , which is not equivalent to $5 \times 5^{-1}$ .