(((a)/(b)))/(c)*(a)/(((b)/(c))) Which of the following is equivalent to the given expression? Choose 1 answer: (A) (a^(2))/(b^(2)) (B) (a^(2))/(c^(2)) (C) (a^(2))/(b^(2)c^(2)) (D) (a^(2)c^(2))/(b^(2))

Multiply by reciprocal: Simplify the given expression by multiplying the numerator and denominator by the reciprocal of the denominator. The given expression is: (((a)/(b)))/(c)*(a)/(((b)/(c))) We can rewrite this as: ((a)/(b)) * (1/c) * (a) * (c/b)Cancel out common factors: Simplify the expression by canceling out common factors. The c in the numerator and the c in the denominator cancel each other out, as do the b in the numerator and the b in the denominator. This leaves us with: (a * a) / (b * b)Use exponents: Rewrite the simplified expression using exponents. The expression (a * a) / (b * b) can be written as: (a^2) / (b^2)Match with answer choices: Match the simplified expression with the given answer choices. The expression (a^2) / (b^2) corresponds to answer choice (A).

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(((a)/(b)))/(c)*(a)/(((b)/(c)))
Which of the following is equivalent to the given expression?
Choose 1 answer:
(A)
(a^(2))/(b^(2))
(B)
(a^(2))/(c^(2))
(C)
(a^(2))/(b^(2)c^(2))
(D)
(a^(2)c^(2))/(b^(2))

$\frac{\left(\frac{a}{b}\right)}{c} \cdot \frac{a}{\left(\frac{b}{c}\right)}$ $\newline$ Which of the following is equivalent to the given expression? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{a^{2}}{b^{2}}$ $\newline$ (B) $\frac{a^{2}}{c^{2}}$ $\newline$ (c) $\frac{a^{2}}{b^{2} c^{2}}$ $\newline$ (D) $\frac{a^{2} c^{2}}{b^{2}}$

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Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

\frac{\left(\frac{a}{b}\right)}{c} \cdot \frac{a}{\left(\frac{b}{c}\right)}

\newline

Which of the following is equivalent to the given expression?

\newline

Choose

1

answer:

\newline

(A)

\frac{a^{2}}{b^{2}}

\newline

(B)

\frac{a^{2}}{c^{2}}

\newline

(c)

\frac{a^{2}}{b^{2} c^{2}}

\newline

(D)

\frac{a^{2} c^{2}}{b^{2}}

Multiply by reciprocal: Simplify the given expression by multiplying the numerator and denominator by the reciprocal of the denominator. $\newline$ The given expression is: $\left(\frac{a}{b}\right)\bigg/\left(\frac{c}{a}\right)\cdot\frac{a}{\left(\frac{b}{c}\right)}$ $\newline$ We can rewrite this as: $\left(\frac{a}{b}\right) \cdot \left(\frac{1}{c}\right) \cdot a \cdot \left(\frac{c}{b}\right)$
Cancel out common factors: Simplify the expression by canceling out common factors. $\newline$ The $c$ in the numerator and the $c$ in the denominator cancel each other out, as do the $b$ in the numerator and the $b$ in the denominator. $\newline$ This leaves us with: $\frac{a \cdot a}{b \cdot b}$
Use exponents: Rewrite the simplified expression using exponents. $\newline$ The expression $(a \cdot a) / (b \cdot b)$ can be written as: $(a^2) / (b^2)$
Match with answer choices: Match the simplified expression with the given answer choices. $\newline$ The expression $(a^2) / (b^2)$ corresponds to answer choice (A).