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Select all the expressions that are equivalent to $10^2 \times 10^5$ . $\newline$ Multi-select Choices: $\newline$ (A) $10^7$ $\newline$ (B) $\frac{1}{10^7}$ $\newline$ (C) $\frac{1}{10^{-7}}$ $\newline$ (D) $\frac{1}{10^{10}}$

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Divide numbers written in scientific notation

Full solution

Q. Select all the expressions that are equivalent to

10^2 \times 10^5

.

\newline

Multi-select Choices:

\newline

(A)

10^7

\newline

(B)

\frac{1}{10^7}

\newline

(C)

\frac{1}{10^{-7}}

\newline

(D)

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

Multiply Powers of $10$ : Step $1$ : Multiply the powers of $10$ . $\newline$ Using the rule of exponents for multiplication, $10^a \times 10^b = 10^{a+b}$ . $\newline$ Calculation: $10^2 \times 10^5 = 10^{2+5} = 10^7$ .
Compare with Choice (A): Step $2$ : Compare with choice (A). $\newline$ $10^7$ matches with choice (A).
Check Choice (B): Step $3$ : Check choice (B). $\newline$ $1/10^7$ is the reciprocal of $10^7$ , not equivalent to multiplying powers of $10$ .
Check Choice (C): Step $4$ : Check choice (C). $\newline$ $1/10^{-7}$ simplifies to $10^7$ , which is equivalent to $10^2 \times 10^5$ .
Check Choice (D): Step $5$ : Check choice (D). $\newline$ $1/10^{10}$ is the reciprocal of $10^{10}$ , not equivalent to $10^2 \times 10^5$ .

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