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(a^(5)l^(2))/(3)*(b)/(a^(2))
Which expression is equivalent to the product for all
a > 0 ?
Choose 1 answer:
(A)
(bl^(2))/(3a^(3))
(B)
(a^(7)l^(2))/(3b)
(c)
(bl^(2))/(3)
(D)
(a^(3)bl^(2))/(3)

$\frac{a^{5} l^{2}}{3} \cdot \frac{b}{a^{2}}$ $\newline$ Which expression is equivalent to the product for all a>0 ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{b l^{2}}{3 a^{3}}$ $\newline$ (B) $\frac{a^{7} l^{2}}{3 b}$ $\newline$ (C) $\frac{b l^{2}}{3}$ $\newline$ (D) $\frac{a^{3} b l^{2}}{3}$

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Compare linear and exponential growth

Full solution

Q.

\frac{a^{5} l^{2}}{3} \cdot \frac{b}{a^{2}}

\newline

Which expression is equivalent to the product for all

a>0

?

\newline

Choose

1

answer:

\newline

(A)

\frac{b l^{2}}{3 a^{3}}

\newline

(B)

\frac{a^{7} l^{2}}{3 b}

\newline

(C)

\frac{b l^{2}}{3}

\newline

(D)

\frac{a^{3} b l^{2}}{3}

Identify properties of exponents: Write down the given expression and identify the properties of exponents that can be used to simplify it. $\newline$ Given expression: $(a^{5}l^{2})/(3)\cdot(b)/(a^{2})$ $\newline$ Properties of exponents to use: $\newline$ - When multiplying powers with the same base, add the exponents. $\newline$ - When dividing powers with the same base, subtract the exponents.
Apply properties of exponents: Apply the properties of exponents to simplify the expression. $\newline$ Simplify the expression by dividing the powers of 'a': $\newline$ $\frac{a^{5} \cdot b \cdot l^{2}}{3 \cdot a^{2}}$ $\newline$ Now, divide the powers of 'a' by subtracting the exponents: $\newline$ $a^{5-2} \cdot b \cdot l^{2} / 3$ $\newline$ This simplifies to: $\newline$ $\frac{a^{3} \cdot b \cdot l^{2}}{3}$
Simplify expression by dividing powers of 'a': Write the simplified expression in the form of the answer choices. $\newline$ The simplified expression is: $\newline$ $\frac{a^{3} \cdot b \cdot l^{2}}{3}$ $\newline$ This matches answer choice (D).

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\newline

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\newline

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\newline

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