Which exponential expression is equivalent to root(3)(a) ? Choose 1 answer: (A) (1)/(a^(3)) (B) a^(3) (C) a^((1)/(3)) (D) (1)/(a^((1)/(3)))

Express Cube Root: We need to express the cube root of a number 'a' in exponential form. The cube root of a number is the same as raising that number to the power of 1/3.Write in Exponential Form: We can write the cube root of 'a' as a^(1/3). This is because the cube root is the inverse operation of raising a number to the power of 3, and in exponential terms, this inverse operation is represented by the fraction 1/3.Match with Given Options: Now we will match our expression a^(1/3) with the given options to find the equivalent expression. (A) (1)/(a^(3)) is not correct because it represents the reciprocal of a raised to the power of 3. (B) a^(3) is not correct because it represents a raised to the power of 3, not the cube root of a. (C) a^((1)/(3)) is correct because it represents the cube root of a. (D) (1)/(a^((1)/(3))) is not correct because it represents the reciprocal of the cube root of a.

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Which exponential expression is equivalent to
root(3)(a) ?
Choose 1 answer:
(A)
(1)/(a^(3))
(B)
a^(3)
(C)
a^((1)/(3))
(D)
(1)/(a^((1)/(3)))

Which exponential expression is equivalent to $\sqrt[3]{a}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{1}{a^{3}}$ $\newline$ (B) $a^{3}$ $\newline$ (C) $a^{\frac{1}{3}}$ $\newline$ (D) $\frac{1}{a^{\frac{1}{3}}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Which exponential expression is equivalent to

\sqrt[3]{a}

\newline

Choose

1

answer:

\newline

(A)

\frac{1}{a^{3}}

\newline

(B)

a^{3}

\newline

(C)

a^{\frac{1}{3}}

\newline

(D)

\frac{1}{a^{\frac{1}{3}}}

Express Cube Root: We need to express the cube root of a number $a$ in exponential form. The cube root of a number is the same as raising that number to the power of $\frac{1}{3}$ .
Write in Exponential Form: We can write the cube root of $a$ as $a^{(1/3)}$ . This is because the cube root is the inverse operation of raising a number to the power of $3$ , and in exponential terms, this inverse operation is represented by the fraction $1/3$ .
Match with Given Options: Now we will match our expression $a^{\frac{1}{3}}$ with the given options to find the equivalent expression. $\newline$ (A) $\frac{1}{a^{3}}$ is not correct because it represents the reciprocal of $a$ raised to the power of $3$ . $\newline$ (B) $a^{3}$ is not correct because it represents $a$ raised to the power of $3$ , not the cube root of $a$ . $\newline$ (C) $a^{\frac{1}{3}}$ is correct because it represents the cube root of $a$ . $\newline$ (D) $\frac{1}{a^{3}}$ $0$ is not correct because it represents the reciprocal of the cube root of $a$ .