Select all the expressions that are equivalent to 7^3 * 10^3. Multi-select Choices: (A)70^3 (B)1/70^-3 (C)70^9 (D)70^6

Calculate Exponents: First, calculate $7^3 \times 10^3$. $7^3 = 343$, $10^3 = 1000$, $343 \times 1000 = 343000$.Check Option (A): Now, check option (A) $70^3$. $70^3 = 343000$. This matches our calculation from Step 1.Evaluate Option (B): Next, evaluate option (B) $1/70^{-3}$. Using the property of exponents, $70^{-3} = \frac{1}{70^3}$, So, $1/70^{-3} = 70^3 = 343000$. This also matches our initial calculation.Check Option (C): Check option (C) $70^9$. This is $70^3 \times 70^3 \times 70^3$, Calculating one $70^3 = 343000$, and raising it to the power of 3 does not equal 343000.

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Calculus

Find derivatives of using multiple formulae

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Q. Select all the expressions that are equivalent to

7^3 \times 10^3

\newline

Multi-select Choices:

\newline

(A)

70^3

\newline

(B)

\frac{1}{70^{-3}}

\newline

(C)

70^9

\newline

(D)

70^6

Calculate Exponents: First, calculate $7^3 \times 10^3$ . $\newline$ $7^3 = 343$ , $\newline$ $10^3 = 1000$ , $\newline$ $343 \times 1000 = 343000$ .
Check Option (A): Now, check option (A) $70^3$ . $\newline$ $70^3 = 343000$ . $\newline$ This matches our calculation from Step $1$ .
Evaluate Option (B): Next, evaluate option (B) $1/70^{-3}$ . $\newline$ Using the property of exponents, $70^{-3} = \frac{1}{70^3}$ , $\newline$ So, $1/70^{-3} = 70^3 = 343000$ . $\newline$ This also matches our initial calculation.
Check Option (C): Check option (C) $70^9$ . $\newline$ This is $70^3 \times 70^3 \times 70^3$ , $\newline$ Calculating one $70^3 = 343000$ , and raising it to the power of $3$ does not equal $343000$ .