Select all the expressions that are equivalent to 12^4 * 12^6. Multi-select Choices: (A)1/12^10 (B)12^10 (C)1/12^24 (D)12^24

Use Exponent Property: To find an expression equivalent to $12^4 \times 12^6$, we use the property of exponents that states when multiplying two powers with the same base, we add the exponents. Calculation: $12^4 \times 12^6 = 12^{4+6} = 12^{10}$.Calculate Result: Now we compare the result $12^{10}$ with each of the given choices to determine which are equivalent. (A) $1/12^{10}$ is not equivalent because it represents the reciprocal of $12^{10}$.Compare with Choices: (B) $12^{10}$ is equivalent because it matches the result of our calculation.Check Choice (A): (C) $1/12^{24}$ is not equivalent because it represents the reciprocal of $12^{24}$, which is not the same as $12^{10}$.Check Choice (B): (D) $12^{24}$ is not equivalent because it represents a much larger number, $12^{24}$, which is not the result of our initial calculation.

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Find derivatives of using multiple formulae

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Q. Select all the expressions that are equivalent to

12^4 \times 12^6

\newline

Multi-select Choices:

\newline

(A)

\frac{1}{12^{10}}

\newline

(B)

12^{10}

\newline

(C)

\frac{1}{12^{24}}

\newline

(D)

12^{24}

Use Exponent Property: To find an expression equivalent to $12^4 \times 12^6$ , we use the property of exponents that states when multiplying two powers with the same base, we add the exponents. $\newline$ Calculation: $12^4 \times 12^6 = 12^{4+6} = 12^{10}$ .
Calculate Result: Now we compare the result $12^{10}$ with each of the given choices to determine which are equivalent. $\newline$ (A) $1/12^{10}$ is not equivalent because it represents the reciprocal of $12^{10}$ .
Compare with Choices: (B) $12^{10}$ is equivalent because it matches the result of our calculation.
Check Choice (A): (C) $1/12^{24}$ is not equivalent because it represents the reciprocal of $12^{24}$ , which is not the same as $12^{10}$ .
Check Choice (B): (D) $12^{24}$ is not equivalent because it represents a much larger number, $12^{24}$ , which is not the result of our initial calculation.