Select all the expressions that are equivalent to 5^-9 * 5^9. Multi-select Choices: (A)5^0 (B)5^-81 (C)1 (D)1/5^0

Simplify Expression: Simplify the expression 5^-9 * 5^9. When multiplying powers with the same base, we add the exponents. 5^-9 * 5^9 = 5^(-9 + 9) = 5^0Find Value: Determine the value of 5^0. Any non-zero number raised to the power of 0 is 1. 5^0 = 1Check Choices: Check the multi-select choices against the simplified expression. (A) 5^0 is equivalent to our simplified expression, which is 1. (B) 5^-81 is not equivalent because the exponents do not add up to 0. (C) 1 is equivalent to our simplified expression, which is 5^0. (D) 1/5^0 is equivalent to 1 because 5^0 is 1 and 1 divided by 1 is 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^{-9} \times 5^{9}

\newline

Multi-select Choices:

\newline

(A)

5^{0}

\newline

(B)

5^{-81}

\newline

(C)

1

\newline

(D)

\frac{1}{5^{0}}

Simplify Expression: Simplify the expression $5^{-9} \times 5^{9}$ . $\newline$ When multiplying powers with the same base, we add the exponents. $\newline$ $5^{-9} \times 5^{9} = 5^{(-9 + 9)} = 5^{0}$
Find Value: Determine the value of $5^0$ . $\newline$ Any non-zero number raised to the power of $0$ is $1$ . $\newline$ $5^0 = 1$
Check Choices: Check the multi-select choices against the simplified expression. $\newline$ (A) $5^0$ is equivalent to our simplified expression, which is $1$ . $\newline$ (B) $5^{-81}$ is not equivalent because the exponents do not add up to $0$ . $\newline$ (C) $1$ is equivalent to our simplified expression, which is $5^0$ . $\newline$ (D) $1/5^0$ is equivalent to $1$ because $5^0$ is $1$ and $1$ divided by $1$ is $1$ .