Which expressions are equivalent to (5^(2))/(5^(8)) ? Choose 2 answers: A (1)/(5^(6)) B 1^(-6) c (5^(2))^(-3) D (5^(2))^(-8)

Simplify expression using laws of exponents: Simplify the expression (5^(2))/(5^(8)) by using the laws of exponents. When dividing powers with the same base, subtract the exponents: 5^(2-8) = 5^(-6).Compare simplified expression with choices: Compare the simplified expression 5^(-6) with the given choices. A. (1)/(5^(6)) is equivalent to 5^(-6) because 1 divided by any number is the reciprocal of that number, which is expressed as a negative exponent.Check choice B: Check choice B, which is 1^(-6). 1 raised to any power is 1, so 1^(-6) = 1, which is not equivalent to 5^(-6).Check choice C: Check choice C, which is (5^(2))^(-3). Using the laws of exponents, (a^b)^c = a^(b*c), so (5^(2))^(-3) = 5^(2*(-3)) = 5^(-6), which is equivalent to the original expression.Check choice D: Check choice D, which is (5^(2))^(-8). Using the laws of exponents, (a^b)^c = a^(b*c), so (5^(2))^(-8) = 5^(2*(-8)) = 5^(-16), which is not equivalent to the original expression.

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Math Problems

Grade 8

Evaluate expressions using properties of exponents

Full solution

Q. Which expressions are equivalent to

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\frac{5^{2}}{5^{8}}

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Choose

2

answers:

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\frac{1}{5^{6}}

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1^{-6}

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(5^{2})^{-3}

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(5^{2})^{-8}

Simplify expression using laws of exponents: Simplify the expression $(5^{2})/(5^{8})$ by using the laws of exponents. $\newline$ When dividing powers with the same base, subtract the exponents: $5^{2-8} = 5^{-6}$ .
Compare simplified expression with choices: Compare the simplified expression $5^{-6}$ with the given choices. $\newline$ A. $(1)/(5^{6})$ is equivalent to $5^{-6}$ because $1$ divided by any number is the reciprocal of that number, which is expressed as a negative exponent.
Check choice B: Check choice B, which is $1^{(-6)}$ . $\newline$ $1$ raised to any power is $1$ , so $1^{(-6)} = 1$ , which is not equivalent to $5^{(-6)}$ .
Check choice C: Check choice C, which is $(5^{2})^{(-3)}$ . $\newline$ Using the laws of exponents, $(a^{b})^{c} = a^{(b*c)}$ , so $(5^{2})^{(-3)} = 5^{(2*(-3))} = 5^{-6}$ , which is equivalent to the original expression.
Check choice D: Check choice D, which is $(5^{2})^{(-8)}$ . $\newline$ Using the laws of exponents, $(a^{b})^{c} = a^{(b*c)}$ , so $(5^{2})^{(-8)} = 5^{(2*(-8))} = 5^{-16}$ , which is not equivalent to the original expression.