Select all the expressions that are equivalent to 10^2 * 10^5. Multi-select Choices: (A)10^7 (B)1/10^7 (C)1/10^-7 (D)1/10^10

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

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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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Math Problems

Grade 8

Divide numbers written in scientific notation

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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 $10^2 \times 10^5$ .