Which expressions are equivalent to 7^(-2)*7^(6) ? Choose 2 answers: A (7^(2))/(7^(-2)) B (7^(6))/(7^(-2)) [C] 7^(-12) D (7^(2))^(2)

Question

Which expressions are equivalent to  7^(-2)*7^(6) ? Choose 2 answers: A  (7^(2))/(7^(-2)) B  (7^(6))/(7^(-2)) [C]  7^(-12) D  (7^(2))^(2)

Bytelearn · Accepted Answer

Apply Exponent Rule: Apply the exponent rule for multiplying powers with the same base. When multiplying powers with the same base, you add the exponents. 7^(-2) * 7^(6) = 7^(-2 + 6) Calculate the sum of the exponents. -2 + 6 = 4 So, 7^(-2) * 7^(6) = 7^(4)Check Answer Choices: Check each answer choice to see if it simplifies to 7^(4). A) (7^(2))/(7^(-2)) Apply the exponent rule for dividing powers with the same base. When dividing powers with the same base, you subtract the exponents. (7^(2))/(7^(-2)) = 7^(2 - (-2)) Calculate the difference of the exponents. 2 - (-2) = 2 + 2 = 4 So, (7^(2))/(7^(-2)) = 7^(4) This expression is equivalent to 7^(-2)*7^(6).Dividing Powers: Check the next answer choice. B) (7^(6))/(7^(-2)) Apply the exponent rule for dividing powers with the same base. (7^(6))/(7^(-2)) = 7^(6 - (-2)) Calculate the difference of the exponents. 6 - (-2) = 6 + 2 = 8 So, (7^(6))/(7^(-2)) = 7^(8) This expression is not equivalent to 7^(-2)*7^(6).Evaluate Expression: Check the next answer choice. [C] 7^(-12) This expression does not involve any operation that would simplify to 7^(4). 7^(-12) is not equivalent to 7^(-2)*7^(6).Raising Power: Check the last answer choice. D) (7^(2))^(2) Apply the exponent rule for raising a power to a power. When raising a power to a power, you multiply the exponents. (7^(2))^(2) = 7^(2 * 2) Calculate the product of the exponents. 2 * 2 = 4 So, (7^(2))^(2) = 7^(4) This expression is equivalent to 7^(-2)*7^(6).

Which expressions are equivalent to $\newline$ $7^{-2} \cdot 7^{6}$ ? $\newline$ Choose $2$ answers: $\newline$ A $\newline$ $\frac{7^{2}}{7^{-2}}$ $\newline$ B $\newline$ $\frac{7^{6}}{7^{-2}}$ $\newline$ C $\newline$ $7^{-12}$ $\newline$ D $\newline$ $(7^{2})^{2}$

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Which expressions are equivalent to \newline7−2⋅767^{-2} \cdot 7^{6}7−2⋅76?\newlineChoose 222 answers:\newlineA \newline727−2\frac{7^{2}}{7^{-2}}7−272​\newlineB \newline767−2\frac{7^{6}}{7^{-2}}7−276​\newlineC \newline7−127^{-12}7−12\newlineD \newline(72)2(7^{2})^{2}(72)2

Which expressions are equivalent to $\newline$ $7^{-2} \cdot 7^{6}$ ? $\newline$ Choose $2$ answers: $\newline$ A $\newline$ $\frac{7^{2}}{7^{-2}}$ $\newline$ B $\newline$ $\frac{7^{6}}{7^{-2}}$ $\newline$ C $\newline$ $7^{-12}$ $\newline$ D $\newline$ $(7^{2})^{2}$