(((l^(5)m^(4)n^(6))/(pq)))/(((l^(5)m^(3)n^(6))/(p^(2)q^(2)))) Which expression is equivalent to the given quotient for all m,n,p,q > 0 ? Choose 1 answer: (A) (1)/(mpq) (B) mpq (c) (l^(10)m^(7)n^(12))/(p^(3)q^(3)) (D) 1

Given expression: We are given the expression: \[ \frac{\left(\frac{l^5m^4n^6}{pq}\right)}{\left(\frac{l^5m^3n^6}{p^2q^2}\right)} \] We need to simplify this complex fraction to find an equivalent expression.Multiply by reciprocal: To simplify a complex fraction, we can multiply the numerator and the denominator by the reciprocal of the denominator. In this case, we multiply by $\frac{p^2q^2}{l^5m^3n^6}$.Expression after multiplication: The expression becomes: \[ \left(\frac{l^5m^4n^6}{pq}\right) \times \left(\frac{p^2q^2}{l^5m^3n^6}\right) \]Multiply numerators and denominators: Now we multiply the numerators together and the denominators together: \[ \frac{l^5m^4n^6 \times p^2q^2}{pq \times l^5m^3n^6} \]Cancel out common terms: We can cancel out the common terms in the numerator and the denominator: \[ \frac{l^{5+0}m^{4-3}n^{6+0}p^{2-1}q^{2-1}}{1} \]Simplify exponents: Simplify the exponents: \[ \frac{l^5m^1n^6p^1q^1}{1} \]Final simplified expression: Since dividing by 1 does not change the value, we can write the simplified expression as: \[ l^5m^1n^6pq \]Check steps: Looking at the answer choices, none of them match our simplified expression exactly. We must have made a mistake in our simplification process. Let's go back and check our steps.

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(((l^(5)m^(4)n^(6))/(pq)))/(((l^(5)m^(3)n^(6))/(p^(2)q^(2))))
Which expression is equivalent to the given quotient for all
m,n,p,q > 0 ?
Choose 1 answer:
(A)
(1)/(mpq)
(B)
mpq
(c)
(l^(10)m^(7)n^(12))/(p^(3)q^(3))
(D) 1

$\frac{\left(\frac{l^{5} m^{4} n^{6}}{p q}\right)}{\left(\frac{l^{5} m^{3} n^{6}}{p^{2} q^{2}}\right)}$ $\newline$ Which expression is equivalent to the given quotient for all m, n, p, q>0 ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{1}{m p q}$ $\newline$ (B) $m p q$ $\newline$ (C) $\frac{l^{10} m^{7} n^{12}}{p^{3} q^{3}}$ $\newline$ (D) $1$

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Algebra 1

Compare linear and exponential growth

Full solution

\frac{\left(\frac{l^{5} m^{4} n^{6}}{p q}\right)}{\left(\frac{l^{5} m^{3} n^{6}}{p^{2} q^{2}}\right)}

\newline

Which expression is equivalent to the given quotient for all

m, n, p, q>0

\newline

Choose

1

answer:

\newline

(A)

\frac{1}{m p q}

\newline

(B)

m p q

\newline

(C)

\frac{l^{10} m^{7} n^{12}}{p^{3} q^{3}}

\newline

(D)

1

Given expression: We are given the expression: $\newline$ $\frac{\left(\frac{l^5m^4n^6}{pq}\right)}{\left(\frac{l^5m^3n^6}{p^2q^2}\right)}$ $\newline$ We need to simplify this complex fraction to find an equivalent expression.
Multiply by reciprocal: To simplify a complex fraction, we can multiply the numerator and the denominator by the reciprocal of the denominator. In this case, we multiply by $\frac{p^2q^2}{l^5m^3n^6}$ .
Expression after multiplication: The expression becomes: $\newline$ $\left(\frac{l^5m^4n^6}{pq}\right) \times \left(\frac{p^2q^2}{l^5m^3n^6}\right)$
Multiply numerators and denominators: Now we multiply the numerators together and the denominators together: $\newline$ $\frac{l^5m^4n^6 \times p^2q^2}{pq \times l^5m^3n^6}$
Cancel out common terms: We can cancel out the common terms in the numerator and the denominator: $\newline$ $\frac{l^{5+0}m^{4-3}n^{6+0}p^{2-1}q^{2-1}}{1}$
Simplify exponents: Simplify the exponents: $\newline$ $\frac{l^5m^1n^6p^1q^1}{1}$
Final simplified expression: Since dividing by $1$ does not change the value, we can write the simplified expression as: $\newline$ $l^5m^1n^6pq$
Check steps: Looking at the answer choices, none of them match our simplified expression exactly. We must have made a mistake in our simplification process. Let's go back and check our steps.