(sqrt(8c^(20)))/(sqrt(32c^(4))) Which of the following is equivalent to the given expression for all c!=0 ? Choose 1 answer: (A) (1)/(2)c^(4) (B) (1)/(2)c^(8) (C) (1)/(4)c^(16) (D) (1)/(4)c^(2)sqrtc

Simplify expression using properties: Simplify the given expression using the properties of radicals and exponents. The given expression is (sqrt(8c^(20)))/(sqrt(32c^(4))). We can simplify the square roots separately first. sqrt(8c^(20)) = sqrt(2^3 * c^(2*10)) = 2 * c^(10) because sqrt(a^2) = a for any positive real number a. sqrt(32c^(4)) = sqrt(2^5 * c^(2*2)) = 4 * c^(2) because sqrt(a^2) = a for any positive real number a.Simplify square roots separately: Divide the simplified square roots. Now we divide (2 * c^(10)) by (4 * c^(2)). (2 * c^(10)) / (4 * c^(2)) = (2/4) * c^(10-2) = (1/2) * c^(8).Divide simplified square roots: Check the answer choices to see which one matches our simplified expression. The expression we found is (1/2) * c^(8), which matches answer choice (B).

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(sqrt(8c^(20)))/(sqrt(32c^(4)))
Which of the following is equivalent to the given expression for all
c!=0 ?
Choose 1 answer:
(A)
(1)/(2)c^(4)
(B)
(1)/(2)c^(8)
(C)
(1)/(4)c^(16)
(D)
(1)/(4)c^(2)sqrtc

$\frac{\sqrt{8 c^{20}}}{\sqrt{32 c^{4}}}$ $\newline$ Which of the following is equivalent to the given expression for all $c \neq 0$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{1}{2} c^{4}$ $\newline$ (B) $\frac{1}{2} c^{8}$ $\newline$ (C) $\frac{1}{4} c^{16}$ $\newline$ (D) $\frac{1}{4} c^{2} \sqrt{c}$

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Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

\frac{\sqrt{8 c^{20}}}{\sqrt{32 c^{4}}}

\newline

Which of the following is equivalent to the given expression for all

c \neq 0

\newline

Choose

1

answer:

\newline

(A)

\frac{1}{2} c^{4}

\newline

(B)

\frac{1}{2} c^{8}

\newline

(C)

\frac{1}{4} c^{16}

\newline

(D)

\frac{1}{4} c^{2} \sqrt{c}

Simplify expression using properties: Simplify the given expression using the properties of radicals and exponents. $\newline$ The given expression is $\frac{\sqrt{8c^{20}}}{\sqrt{32c^{4}}}$ . $\newline$ We can simplify the square roots separately first. $\newline$ $\sqrt{8c^{20}} = \sqrt{2^3 \cdot c^{2\cdot10}} = 2 \cdot c^{10}$ because $\sqrt{a^2} = a$ for any positive real number $a$ . $\newline$ $\sqrt{32c^{4}} = \sqrt{2^5 \cdot c^{2\cdot2}} = 4 \cdot c^{2}$ because $\sqrt{a^2} = a$ for any positive real number $a$ .
Simplify square roots separately: Divide the simplified square roots. $\newline$ Now we divide $(2 \cdot c^{10})$ by $(4 \cdot c^{2})$ . $\newline$ $(2 \cdot c^{10}) / (4 \cdot c^{2}) = (2/4) \cdot c^{(10-2)} = (1/2) \cdot c^{8}$ .
Divide simplified square roots: Check the answer choices to see which one matches our simplified expression. $\newline$ The expression we found is $(\frac{1}{2}) \cdot c^{8}$ , which matches answer choice (B).