Select the expression that is equivalent to (1)/((2x^(2)+7)^((1)/(2))) (1)/(sqrt((2x^(2)+7)^(2))) (1)/(sqrt(2x^(2)+7)) sqrt((2x^(2)+7)^(2)) sqrt(2x^(2)+7)

Rewritten Expression: We are given the expression (1)/((2x^(2)+7)^((1)/(2))) and we need to find an equivalent expression. The exponent (1/2) is equivalent to the square root. So, we can rewrite the expression as: (1)/(sqrt(2x^(2)+7))Examine Other Options: Now let's examine the other options to see if any of them are equivalent to our rewritten expression: Option A: (1)/(sqrt((2x^(2)+7)^(2))) - This simplifies to (1)/(2x^(2)+7), which is not equivalent to our expression. Option B: (1)/(sqrt(2x^(2)+7)) - This is the same as our rewritten expression, so it is equivalent. Option C: sqrt((2x^(2)+7)^(2)) - This simplifies to 2x^(2)+7, which is not equivalent to our expression. Option D: sqrt(2x^(2)+7) - This is the square root of the denominator of our original expression, not the entire expression, so it is not equivalent.

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Select the expression that is equivalent to
(1)/((2x^(2)+7)^((1)/(2)))

(1)/(sqrt((2x^(2)+7)^(2)))

(1)/(sqrt(2x^(2)+7))

sqrt((2x^(2)+7)^(2))

sqrt(2x^(2)+7)

Select the expression that is equivalent to $\frac{1}{\left(2 x^{2}+7\right)^{\frac{1}{2}}}$ $\newline$ $\frac{1}{\sqrt{\left(2 x^{2}+7\right)^{2}}}$ $\newline$ $\frac{1}{\sqrt{2 x^{2}+7}}$ $\newline$ $\sqrt{\left(2 x^{2}+7\right)^{2}}$ $\newline$ $\sqrt{2 x^{2}+7}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the expression that is equivalent to

\frac{1}{\left(2 x^{2}+7\right)^{\frac{1}{2}}}

\newline

\frac{1}{\sqrt{\left(2 x^{2}+7\right)^{2}}}

\newline

\frac{1}{\sqrt{2 x^{2}+7}}

\newline

\sqrt{\left(2 x^{2}+7\right)^{2}}

\newline

\sqrt{2 x^{2}+7}

Rewritten Expression: We are given the expression $(1)/((2x^{2}+7)^{(1)/(2)})$ and we need to find an equivalent expression. The exponent $(1/2)$ is equivalent to the square root. So, we can rewrite the expression as: $(1)/(\sqrt{2x^{2}+7})$
Examine Other Options: Now let's examine the other options to see if any of them are equivalent to our rewritten expression: $\newline$ Option A: $(1)/(\sqrt{((2x^{2}+7)^{2})})$ - This simplifies to $(1)/(2x^{2}+7)$ , which is not equivalent to our expression. $\newline$ Option B: $(1)/(\sqrt{2x^{2}+7})$ - This is the same as our rewritten expression, so it is equivalent. $\newline$ Option C: $\sqrt{(2x^{2}+7)^{2}}$ - This simplifies to $2x^{2}+7$ , which is not equivalent to our expression. $\newline$ Option D: $\sqrt{2x^{2}+7}$ - This is the square root of the denominator of our original expression, not the entire expression, so it is not equivalent.