Select all the expressions that are equivalent to 6^4 * 6^8. Multi-select Choices: (A)1/6^32 (B)6^12 (C)6^32 (D)1/6^-12

Combine Exponents: Use the property of exponents that states $a^m \times a^n = a^{m+n}$ to combine $6^4$ and $6^8$. Calculation: $6^4 \times 6^8 = 6^{4+8} = 6^{12}$Check Options: Check each of the given options to see if they are equivalent to $6^{12}$. Option (A) $1/6^{32}$ is not equivalent because it represents the reciprocal of $6^{32}$, not $6^{12}$.Option (A): Option (B) $6^{12}$ is equivalent because it matches the result from Step 1.Option (B): Option (C) $6^{32}$ is not equivalent because it represents $6$ raised to the power of $32$, which is not the sum of $4$ and $8$.Option (C): Option (D) $1/6^{-12}$ is equivalent because using the property of negative exponents $a^{-n} = 1/a^n$, it simplifies to $6^{12}$. Calculation: $1/6^{-12} = 6^{12}$

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Select all the expressions that are equivalent to $6^4 \times 6^8$ . $\newline$ Multi-select Choices: $\newline$ (A) $\frac{1}{6^{32}}$ $\newline$ (B) $6^{12}$ $\newline$ (C) $6^{32}$ $\newline$ (D) $\frac{1}{6^{-12}}$

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Math Problems

Algebra 2

Simplify rational expressions

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Q. Select all the expressions that are equivalent to

6^4 \times 6^8

\newline

Multi-select Choices:

\newline

(A)

\frac{1}{6^{32}}

\newline

(B)

6^{12}

\newline

(C)

6^{32}

\newline

(D)

\frac{1}{6^{-12}}

Combine Exponents: Use the property of exponents that states $a^m \times a^n = a^{m+n}$ to combine $6^4$ and $6^8$ . $\newline$ Calculation: $6^4 \times 6^8 = 6^{4+8} = 6^{12}$
Check Options: Check each of the given options to see if they are equivalent to $6^{12}$ . $\newline$ Option (A) $1/6^{32}$ is not equivalent because it represents the reciprocal of $6^{32}$ , not $6^{12}$ .
Option (A): Option (B) $6^{12}$ is equivalent because it matches the result from Step $1$ .
Option (B): Option (C) $6^{32}$ is not equivalent because it represents $6$ raised to the power of $32$ , which is not the sum of $4$ and $8$ .
Option (C): Option (D) $1/6^{-12}$ is equivalent because using the property of negative exponents $a^{-n} = 1/a^n$ , it simplifies to $6^{12}$ . $\newline$ Calculation: $1/6^{-12} = 6^{12}$