Given x > 0, the expression sqrt(x^(4)) is equivalent to x^(2) xsqrtx x^(2)sqrtx x

Question Prompt: Question prompt: What is the equivalent expression for sqrt(x^(4)) given x > 0?Properties: Understand the properties of square roots and exponents. The square root of a number is the value that, when multiplied by itself, gives the original number. For any positive real number a, sqrt(a^2) = a. This is because (sqrt(a))^2 = a^2, and since we are given that x > 0, we can apply this property directly.Apply Property: Apply the property to the given expression. We have sqrt(x^(4)). According to the property from Step 1, this simplifies to x^(4/2) because the square root is the same as raising to the power of 1/2, and when we multiply the exponents, we get (4 * 1/2) = 2.Simplify Expression: Simplify the expression. Simplifying x^(4/2) gives us x^2. Since x is positive, we do not need to consider the absolute value, and we can directly state that sqrt(x^(4)) = x^2.

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Given
x > 0, the expression
sqrt(x^(4)) is equivalent to

x^(2)

xsqrtx

x^(2)sqrtx

x

Given x>0 , the expression $\sqrt{x^{4}}$ is equivalent to $\newline$ $x^{2}$ $\newline$ $x \sqrt{x}$ $\newline$ $x^{2} \sqrt{x}$ $\newline$ $x$

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Calculus

Find indefinite integrals using the substitution

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Q. Given

x>0

, the expression

\sqrt{x^{4}}

is equivalent to

\newline

x^{2}

\newline

x \sqrt{x}

\newline

x^{2} \sqrt{x}

\newline

x

Question Prompt: Question prompt: What is the equivalent expression for $\sqrt{x^{4}}$ given x > 0?
Properties: Understand the properties of square roots and exponents. $\newline$ The square root of a number is the value that, when multiplied by itself, gives the original number. For any positive real number $a$ , $\sqrt{a^2} = a$ . This is because $(\sqrt{a})^2 = a^2$ , and since we are given that x > 0, we can apply this property directly.
Apply Property: Apply the property to the given expression. $\newline$ We have $\sqrt{x^{4}}$ . According to the property from Step $1$ , this simplifies to $x^{\frac{4}{2}}$ because the square root is the same as raising to the power of $\frac{1}{2}$ , and when we multiply the exponents, we get $(4 \times \frac{1}{2}) = 2$ .
Simplify Expression: Simplify the expression. $\newline$ Simplifying $x^{(4/2)}$ gives us $x^2$ . Since $x$ is positive, we do not need to consider the absolute value, and we can directly state that $\sqrt{x^{4}} = x^2$ .