Select all the expressions that are equivalent to 5 * 5^-1. Multi-select Choices: (A)1/5^0 (B)5^-1 (C)1 (D)1/5^-1

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

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Math Problems

Algebra 1

Simplify exponential expressions using exponent rules

Full solution

Q. Select all the expressions that are equivalent to

5 \times 5^{-1}

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Multi-select Choices:

\newline

(A)

\frac{1}{5^0}

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(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 $5 \times 5^{-1}$ .