Which exponential expression is equivalent to root(4)(x^(3)) ? Choose 1 answer: (A) (x^(3))/(x^(4)) (B) x^((4)/(3)) (C) x^((3)/(4)) (D) (x^(4))/(x^(3))

Identify Equivalent Expression: We are looking for an expression equivalent to the fourth root of x cubed, which can be written as x^(3/4).Apply Exponent Rule: The fourth root of x cubed is the same as raising x to the power of 3 and then taking the fourth root, which can be expressed as (x^3)^(1/4).Simplify Exponential Expression: Using the property of exponents that states (a^m)^(n) = a^(m*n), we can simplify (x^3)^(1/4) to x^(3*1/4).Compare with Options: Multiplying the exponents, we get x^(3/4).Now we compare the result with the given options. The expression x^(3/4) matches option (C) x^(3/4).

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Which exponential expression is equivalent to $\sqrt[4]{x^3}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{x^3}{x^4}$ $\newline$ (B) $x^{\frac{4}{3}}$ $\newline$ (C) $x^{\frac{3}{4}}$ $\newline$ (D) $\frac{x^4}{x^3}$

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Math Problems

Algebra 1

Multiplication with rational exponents

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Q. Which exponential expression is equivalent to

\sqrt[4]{x^3}

\newline

Choose

1

answer:

\newline

(A)

\frac{x^3}{x^4}

\newline

(B)

x^{\frac{4}{3}}

\newline

(C)

x^{\frac{3}{4}}

\newline

(D)

\frac{x^4}{x^3}

Identify Equivalent Expression: We are looking for an expression equivalent to the fourth root of $x$ cubed, which can be written as $x^{\frac{3}{4}}$ .
Apply Exponent Rule: The fourth root of $x$ cubed is the same as raising $x$ to the power of $3$ and then taking the fourth root, which can be expressed as $(x^3)^{\frac{1}{4}}$ .
Simplify Exponential Expression: Using the property of exponents that states $(a^m)^n = a^{m*n}$ , we can simplify $(x^3)^{1/4}$ to $x^{3*1/4}$ .
Compare with Options: Multiplying the exponents, we get $x^{\frac{3}{4}}$ .
Compare with Options: Multiplying the exponents, we get $x^{\frac{3}{4}}$ .Now we compare the result with the given options. The expression $x^{\frac{3}{4}}$ matches option (C) $x^{\frac{3}{4}}$ .