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))

Understanding the fourth root: Understand the meaning of the fourth root in terms of exponents. The fourth root of a number is the same as raising that number to the power of 1/4.Applying the exponent rule: Apply the exponent rule for roots to the given expression. The fourth root of x cubed can be written as (x^3)^(1/4).Using the power of a power rule: Use the power of a power rule. When you raise a power to a power, you multiply the exponents. So, (x^3)^(1/4) is x^(3*(1/4)).Performing the multiplication of exponents: Perform the multiplication of the exponents. 3 * (1/4) = 3/4.Writing the final expression: Write the final expression. Therefore, the fourth root of x cubed is x^(3/4).

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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))

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

Grade 7

Identify equivalent linear expressions I

Full solution

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}}

Understanding the fourth root: Understand the meaning of the fourth root in terms of exponents. $\newline$ The fourth root of a number is the same as raising that number to the power of $\frac{1}{4}$ .
Applying the exponent rule: Apply the exponent rule for roots to the given expression. $\newline$ The fourth root of $x$ cubed can be written as $(x^3)^{\frac{1}{4}}$ .
Using the power of a power rule: Use the power of a power rule. $\newline$ When you raise a power to a power, you multiply the exponents. So, $(x^3)^{\frac{1}{4}}$ is $x^{3\cdot\frac{1}{4}}$ .
Performing the multiplication of exponents: Perform the multiplication of the exponents. $3 \times \left(\frac{1}{4}\right) = \frac{3}{4}.$
Writing the final expression: Write the final expression. $\newline$ Therefore, the fourth root of $x$ cubed is $x^{(3/4)}$ .