(((ℓ^(5)n^(2))/(ℓ^(7)n)))/(((ℓ^(3)n^(9))/(ℓn^(3)))) Which expression is equivalent to the given quotient for all ℓ 4 ? Choose 1 answer: (A) 0 (B) 1 (c) ℓ^(4)n^(5) (D) (1)/(ℓ^(4)n^(5))

Simplify expression by dividing: Simplify the given expression by dividing the numerators and denominators separately. The given expression is: (((ℓ^(5)n^(2))/(ℓ^(7)n)))/(((ℓ^(3)n^(9))/(ℓn^(3)))) We can simplify the expression by dividing the exponents with the same base using the property a^(m)/a^(n) = a^(m-n).Apply exponent rules to numerator: Apply the exponent rules to the numerator. Simplify ℓ^(5)n^(2) divided by ℓ^(7)n: ℓ^(5-7)n^(2-1) = ℓ^(-2)n^(1)Apply exponent rules to denominator: Apply the exponent rules to the denominator. Simplify ℓ^(3)n^(9) divided by ℓn^(3): ℓ^(3-1)n^(9-3) = ℓ^(2)n^(6)Divide numerator by denominator: Now divide the simplified numerator by the simplified denominator. Divide ℓ^(-2)n^(1) by ℓ^(2)n^(6): (ℓ^(-2)n^(1))/(ℓ^(2)n^(6))Apply exponent rules to division: Apply the exponent rules to the division of the simplified numerator and denominator. ℓ^(-2-2)n^(1-6) = ℓ^(-4)n^(-5)Rewrite expression with positive exponents: Rewrite the expression with positive exponents. ℓ^(-4)n^(-5) can be rewritten as (1)/(ℓ^(4)n^(5)).

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(((ℓ^(5)n^(2))/(ℓ^(7)n)))/(((ℓ^(3)n^(9))/(ℓn^(3))))
Which expression is equivalent to the given quotient for all
ℓ < -2 and
n > 4 ?
Choose 1 answer:
(A) 0
(B) 1
(c)
ℓ^(4)n^(5)
(D)
(1)/(ℓ^(4)n^(5))

$\frac{\left(\frac{\ell^{5} n^{2}}{\ell^{7} n}\right)}{\left(\frac{\ell^{3} n^{9}}{\ell n^{3}}\right)}$ $\newline$ Which expression is equivalent to the given quotient for all \ell<-2 and n>4 ? $\newline$ Choose $1$ answer: $\newline$ (A) $0$ $\newline$ (B) $1$ $\newline$ (C) $\ell^{4} n^{5}$ $\newline$ (D) $\frac{1}{\ell^{4} n^{5}}$

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Math Problems

Algebra 1

Compare linear, exponential, and quadratic growth

Full solution

\frac{\left(\frac{\ell^{5} n^{2}}{\ell^{7} n}\right)}{\left(\frac{\ell^{3} n^{9}}{\ell n^{3}}\right)}

\newline

Which expression is equivalent to the given quotient for all

\ell<-2

and

n>4

\newline

Choose

1

answer:

\newline

(A)

0

\newline

(B)

1

\newline

(C)

\ell^{4} n^{5}

\newline

(D)

\frac{1}{\ell^{4} n^{5}}

Simplify expression by dividing: Simplify the given expression by dividing the numerators and denominators separately. $\newline$ The given expression is: $\newline$ $\left(\frac{\ell^{5}n^{2}}{\ell^{7}n}\right)\bigg/\left(\frac{\ell^{3}n^{9}}{\ell n^{3}}\right)$ $\newline$ We can simplify the expression by dividing the exponents with the same base using the property $a^{m}/a^{n} = a^{m-n}$ .
Apply exponent rules to numerator: Apply the exponent rules to the numerator. $\newline$ Simplify $\ell^{5}n^{2}$ divided by $\ell^{7}n$ : $\newline$ $\ell^{5-7}n^{2-1} = \ell^{-2}n^{1}$
Apply exponent rules to denominator: Apply the exponent rules to the denominator. $\newline$ Simplify $\ell^{3}n^{9}$ divided by $\ell n^{3}$ : $\newline$ $\ell^{(3-1)}n^{(9-3)} = \ell^{2}n^{6}$
Divide numerator by denominator: Now divide the simplified numerator by the simplified denominator. $\newline$ Divide $\ell^{-2}n^{1}$ by $\ell^{2}n^{6}$ : $\newline$ $\frac{\ell^{-2}n^{1}}{\ell^{2}n^{6}}$
Apply exponent rules to division: Apply the exponent rules to the division of the simplified numerator and denominator. $\newline$ $\ell^{(-2-2)}n^{(1-6)} = \ell^{-4}n^{-5}$
Rewrite expression with positive exponents: Rewrite the expression with positive exponents. $\newline$ $\ell^{-4}n^{-5}$ can be rewritten as $\frac{1}{\ell^{4}n^{5}}$ .