(((1)/(9))^(124))/(((1)/(3))^(72)) Which of the following values is equal to the given value? Choose 1 answer: (A) 3^(-176) (B) 3^(-52) (C) 3^(52) (D) 3^(176)

Simplify expression using exponents: Simplify the given expression using the properties of exponents. The given expression is (((1)/(9))^(124))/(((1)/(3))^(72)). We know that (1/9) = 3^(-2) and (1/3) = 3^(-1). Let's rewrite the expression using these equivalences. (((1)/(9))^(124))/(((1)/(3))^(72)) = (3^(-2))^124 / (3^(-1))^72 Now, apply the power of a power rule (a^(m))^n = a^(m*n). (3^(-2))^124 = 3^(-2*124) = 3^(-248) (3^(-1))^72 = 3^(-1*72) = 3^(-72) So the expression becomes 3^(-248) / 3^(-72).Apply power of a power rule: Apply the quotient of powers rule to simplify the expression further. The quotient of powers rule states that a^(m) / a^(n) = a^(m-n) when a is not equal to 0. 3^(-248) / 3^(-72) = 3^(-248 - (-72)) = 3^(-248 + 72) = 3^(-176).Apply quotient of powers rule: Match the simplified expression to one of the given choices. The simplified expression is 3^(-176), which corresponds to choice (A) 3^(-176).

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(((1)/(9))^(124))/(((1)/(3))^(72))
Which of the following values is equal to the given value?
Choose 1 answer:
(A)
3^(-176)
(B)
3^(-52)
(C)
3^(52)
(D)
3^(176)

$\frac{\left(\frac{1}{9}\right)^{124}}{\left(\frac{1}{3}\right)^{72}}$ $\newline$ Which of the following values is equal to the given value? $\newline$ Choose $1$ answer: $\newline$ (A) $3^{-176}$ $\newline$ (B) $3^{-52}$ $\newline$ (C) $3^{52}$ $\newline$ (D) $3^{176}$

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Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

\frac{\left(\frac{1}{9}\right)^{124}}{\left(\frac{1}{3}\right)^{72}}

\newline

Which of the following values is equal to the given value?

\newline

Choose

1

answer:

\newline

(A)

3^{-176}

\newline

(B)

3^{-52}

\newline

(C)

3^{52}

\newline

(D)

3^{176}

Simplify expression using exponents: Simplify the given expression using the properties of exponents. $\newline$ The given expression is $\left(\frac{1}{9}\right)^{124}/\left(\frac{1}{3}\right)^{72}$ . We know that $\left(\frac{1}{9}\right) = 3^{-2}$ and $\left(\frac{1}{3}\right) = 3^{-1}$ . Let's rewrite the expression using these equivalences. $\newline$ $\left(\frac{1}{9}\right)^{124}/\left(\frac{1}{3}\right)^{72} = \left(3^{-2}\right)^{124} / \left(3^{-1}\right)^{72}$ $\newline$ Now, apply the power of a power rule $(a^{m})^{n} = a^{m*n}$ . $\newline$ $\left(3^{-2}\right)^{124} = 3^{-2*124} = 3^{-248}$ $\newline$ $\left(3^{-1}\right)^{72} = 3^{-1*72} = 3^{-72}$ $\newline$ So the expression becomes $3^{-248} / 3^{-72}$ .
Apply power of a power rule: Apply the quotient of powers rule to simplify the expression further. $\newline$ The quotient of powers rule states that $a^{m} / a^{n} = a^{m-n}$ when $a \neq 0$ . $\newline$ $3^{-248} / 3^{-72} = 3^{-248 - (-72)} = 3^{-248 + 72} = 3^{-176}$ .
Apply quotient of powers rule: Match the simplified expression to one of the given choices. $\newline$ The simplified expression is $3^{-176}$ , which corresponds to choice (A) $3^{-176}$ .