5^((1)/(3))-5^((4)/(3)) Which of the following expressions is equivalent to the given expression? Choose 1 answer: (A) -4*5^((1)/(3)) (B) -root(3)(620) (C) 5^((1)/(4)) (D) (1)/(5)

Analyze given expression: First, let's analyze the given expression: 5^((1)/(3))-5^((4)/(3)). We notice that both terms have the base of 5, but different exponents. The second term can be rewritten using the property of exponents that states a^(m/n) = (a^m)^(1/n). So, 5^((4)/(3)) is the same as (5^4)^(1/3).Rewrite second term: Now, let's rewrite the second term using the property mentioned above: 5^((1)/(3))-(5^4)^(1/3). Since 5^4 = 625, we can substitute this into our expression: 5^((1)/(3))-(625)^(1/3).Recognize cube root: We recognize that (625)^(1/3) is the cube root of 625. The cube root of 625 is 5^((4)/(3)), which is 5^((1)/(3)) * 5. Therefore, (625)^(1/3) = 5^((1)/(3)) * 5.Factor out common term: Substituting back into our expression, we have: 5^((1)/(3)) - (5^((1)/(3)) * 5). We can factor out 5^((1)/(3)) from both terms, which gives us: 5^((1)/(3)) * (1 - 5).Simplify expression: Now, we simplify the expression inside the parentheses: 1 - 5 equals -4. So, our expression becomes: 5^((1)/(3)) * (-4).We have now simplified the original expression to -4 * 5^((1)/(3)), which matches choice (A) from the provided options.

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5^((1)/(3))-5^((4)/(3))
Which of the following expressions is equivalent to the given expression?
Choose 1 answer:
(A)
-4*5^((1)/(3))
(B)
-root(3)(620)
(C)
5^((1)/(4))
(D)
(1)/(5)

$5^{\frac{1}{3}}-5^{\frac{4}{3}}$ $\newline$ Which of the following expressions is equivalent to the given expression? $\newline$ Choose $1$ answer: $\newline$ (A) $-4 \cdot 5^{\frac{1}{3}}$ $\newline$ ( $)-\sqrt[3]{620}$ $\newline$ (C) $5^{\frac{1}{4}}$ $\newline$ (D) $\frac{1}{5}$

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Full solution

5^{\frac{1}{3}}-5^{\frac{4}{3}}

\newline

Which of the following expressions is equivalent to the given expression?

\newline

Choose

1

answer:

\newline

(A)

-4 \cdot 5^{\frac{1}{3}}

\newline

(

)-\sqrt[3]{620}

\newline

(C)

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

\newline

(D)

\frac{1}{5}

Analyze given expression: First, let's analyze the given expression: $5^{\frac{1}{3}}-5^{\frac{4}{3}}$ . We notice that both terms have the base of $5$ , but different exponents. The second term can be rewritten using the property of exponents that states $a^{\frac{m}{n}} = (a^m)^{\frac{1}{n}}$ . So, $5^{\frac{4}{3}}$ is the same as $(5^4)^{\frac{1}{3}}$ .
Rewrite second term: Now, let's rewrite the second term using the property mentioned above: $5^{\frac{1}{3}} - (5^4)^{\frac{1}{3}}$ . Since $5^4 = 625$ , we can substitute this into our expression: $5^{\frac{1}{3}} - (625)^{\frac{1}{3}}$ .
Recognize cube root: We recognize that $(625)^{\frac{1}{3}}$ is the cube root of $625$ . The cube root of $625$ is $5^{\frac{4}{3}}$ , which is $5^{\frac{1}{3}} \times 5$ . Therefore, $(625)^{\frac{1}{3}} = 5^{\frac{1}{3}} \times 5$ .
Factor out common term: Substituting back into our expression, we have: $5^{\frac{1}{3}} - \left(5^{\frac{1}{3}} \times 5\right)$ . We can factor out $5^{\frac{1}{3}}$ from both terms, which gives us: $5^{\frac{1}{3}} \times (1 - 5)$ .
Simplify expression: Now, we simplify the expression inside the parentheses: $1 - 5$ equals $-4$ . So, our expression becomes: $5^{\left(\frac{1}{3}\right)} \cdot (-4)$ .
Simplify expression: Now, we simplify the expression inside the parentheses: $1 - 5$ equals $-4$ . So, our expression becomes: $5^{(1/3)} \cdot (-4)$ .We have now simplified the original expression to $-4 \cdot 5^{(1/3)}$ , which matches choice (A) from the provided options.