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Select all the expressions that are equivalent to $\frac{10^4}{10^4}$ . $\newline$ Multi-select Choices: $\newline$ (A) $10$ $\newline$ (B) $10^8$ $\newline$ (C) $1$ $\newline$ (D) $10^{-6} \times 10^6$

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Divide numbers written in scientific notation

Full solution

Q. Select all the expressions that are equivalent to

\frac{10^4}{10^4}

.

\newline

Multi-select Choices:

\newline

(A)

10

\newline

(B)

10^8

\newline

(C)

1

\newline

(D)

10^{-6} \times 10^6

Simplify Expression: Step $1$ : Simplify the given expression. $\newline$ Calculation: $10^4 / 10^4 = 10^{4-4} = 10^0$ $\newline$ Reasoning: Using the rule of exponents, subtract the exponents when dividing like bases.
Evaluate Exponent: Step $2$ : Evaluate $10^0$ . $\newline$ Calculation: $10^0 = 1$ $\newline$ Reasoning: Any number raised to the power of zero is $1$ .
Compare Choices: Step $3$ : Compare each choice to see if it equals $1$ . $\newline$ (A) $10$ -> Calculation: $10 \neq 1$ $\newline$ (B) $10^8$ -> Calculation: $10^8 \neq 1$ $\newline$ (C) $1$ -> Calculation: $1 = 1$ $\newline$ (D) $10^{-6} \times 10^6$ -> Calculation: $10^{(-6+6)} = 10^0 = 1$ $\newline$ Reasoning: Apply the rule of exponents for multiplication, add the exponents.

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