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Select all the expressions that are equivalent to $10^{-6} \times 10^{9}$ . $\newline$ Multi-select Choices: $\newline$ (A) $\frac{1}{10^{-54}}$ $\newline$ (B) $10^{-54}$ $\newline$ (C) $10^{3}$ $\newline$ (D) $\frac{1}{10^{3}}$

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Simplify exponential expressions using exponent rules

Full solution

Q. Select all the expressions that are equivalent to

10^{-6} \times 10^{9}

.

\newline

Multi-select Choices:

\newline

(A)

\frac{1}{10^{-54}}

\newline

(B)

10^{-54}

\newline

(C)

10^{3}

\newline

(D)

\frac{1}{10^{3}}

Simplify Expression: Step $1$ : Simplify the expression $10^{-6} \times 10^{9}$ . We add the exponents since the bases are the same. $10^{-6} \times 10^{9} = 10^{(-6 + 9)} = 10^{3}$
Compare to Choices: Step $2$ : Compare the simplified expression to the choices. $\newline$ $10^3$ should be matched with the given options. $\newline$ (A) $\frac{1}{10^{-54}}$ is not equal to $10^3$ . $\newline$ (B) $10^{-54}$ is not equal to $10^3$ . $\newline$ (C) $10^3$ is exactly equal to $10^3$ . $\newline$ (D) $\frac{1}{10^3}$ is not equal to $10^3$ ; it's $\frac{1}{1000}$ .

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