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)

Apply Exponent Rules: To find expressions equivalent to 7^(-2)*7^(6), we need to apply the exponent rules, specifically the rule that states when multiplying expressions with the same base, we add the exponents. Calculation: 7^(-2)*7^(6) = 7^(-2+6) = 7^(4)Evaluate Answer Choices: Now let's evaluate each answer choice to see if it simplifies to 7^(4). Choice A: (7^(2))/(7^(-2)) Using the exponent rule for division, which states that when dividing expressions with the same base, we subtract the exponents, we get: (7^(2))/(7^(-2)) = 7^(2 - (-2)) = 7^(2 + 2) = 7^(4)Choice A Calculation: Choice B: (7^(6))/(7^(-2)) Again, using the exponent rule for division: (7^(6))/(7^(-2)) = 7^(6 - (-2)) = 7^(6 + 2) = 7^(8) This expression simplifies to 7^(8), not 7^(4).Choice B Calculation: Choice C: 7^(-12) This expression is simply 7 raised to the power of -12, which is not equivalent to 7^(4).Choice C Calculation: Choice D: (7^(2))^(2) Using the exponent rule for raising a power to a power, which states that we multiply the exponents, we get: (7^(2))^(2) = 7^(2*2) = 7^(4)

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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)

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

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Math Problems

Algebra 1

Transformations of functions

Full solution

Q. Which expressions are equivalent to

7^{-2} \cdot 7^{6}

\newline

Choose

2

answers:

\newline

\frac{7^{2}}{7^{-2}}

\newline

\frac{7^{6}}{7^{-2}}

\newline

7^{-12}

\newline

\left(7^{2}\right)^{2}

Apply Exponent Rules: To find expressions equivalent to $7^{-2}\times7^{6}$ , we need to apply the exponent rules, specifically the rule that states when multiplying expressions with the same base, we add the exponents. $\newline$ Calculation: $7^{-2}\times7^{6} = 7^{-2+6} = 7^{4}$
Evaluate Answer Choices: Now let's evaluate each answer choice to see if it simplifies to $7^{4}$ . $\newline$ Choice A: $(7^{2})/(7^{-2})$ $\newline$ Using the exponent rule for division, which states that when dividing expressions with the same base, we subtract the exponents, we get: $\newline$ $(7^{2})/(7^{-2}) = 7^{2 - (-2)} = 7^{2 + 2} = 7^{4}$
Choice A Calculation: Choice B: $(7^{6})/(7^{-2})$ $\newline$ Again, using the exponent rule for division: $\newline$ $(7^{6})/(7^{-2}) = 7^{6 - (-2)} = 7^{6 + 2} = 7^{8}$ $\newline$ This expression simplifies to $7^{8}$ , not $7^{4}$ .
Choice B Calculation: Choice C: $7^{-12}$ $\newline$ This expression is simply $7$ raised to the power of $-12$ , which is not equivalent to $7^{4}$ .
Choice C Calculation: Choice D: $(7^{2})^{2}$ $\newline$ Using the exponent rule for raising a power to a power, which states that we multiply the exponents, we get: $\newline$ $(7^{2})^{2} = 7^{2*2} = 7^{4}$