Use the product rule to multiply the following.7m24⋅2n4\sqrt[4]{7m^2}\cdot\sqrt[4]{2n}

14m2n4\sqrt[4]{$$14m^2n$$}414m2n

Use the product rule to multiply the following. 7 m 2 4 ⋅ 2 n 4 \sqrt[4]{7m^2}\cdot\sqrt[4]{2n}

we're asked to use the product rule to multiply the following. We have the fourth root of seven m squared times the fourth root of two n. So we're gonna go ahead and apply our product rule in order to condense the product of these two radicals into just one. So rewriting this here, this is going to be the fourth root because remember that's what both of these are. And then doing that multiplication underneath that one radical, this is seven m squared times two n. Doing some further simplification here, we can go ahead and multiply that seven times two to give us 14. So this becomes the fourth root of 14 m squared n, and that's our solution. Having used our product rule for nth roots to do that multiplication. Let us know if you have any questions.

Use the product rule to multiply the following.7m24⋅2n4\sqrt[4]{$$7m^2$$}\cdot\sqrt[4]{2n}

14m2n4\sqrt[4]{$$14m^2n$$}414m2n

7m2+2n4\sqrt[4]{$$7m^2+2n$$}47m2+2n

(14m24)n\left(\sqrt[4]{$$14m^2$$}\right)n(414m2)n

7m24+2n4\sqrt[4]{$$7m^2$$}+\sqrt[4]{2n}47m2+42n

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Simplifying Radical Expressions

Beginning & Intermediate Algebra

11. Roots, Radicals, and Complex Numbers

Simplifying Radical Expressions

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Multiple Choice

Use the product rule to multiply the following.
$\sqrt[4]{7 m^{2}} \cdot \sqrt[4]{2 n}$

$$\sqrt$[4]{7m^2+2n}$

$$\sqrt$[4]{14m^2n}$

$$\left$($\sqrt$[4]{14m^2}$\right$)n$

$$\sqrt$[4]{7m^2}+$\sqrt$[4]{2n}$

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검증된 단계별 안내

Identify the expression to multiply: $\sqrt[4]{7m^{2}} \cdot \sqrt[4]{2n}$.

Recall the product rule for radicals with the same index: $\sqrt[n]{a} \cdot \sqrt[n]{b} = \sqrt[n]{a \cdot b}$.

Apply the product rule by multiplying the radicands (the expressions inside the roots): $7m^{2} \times 2n = 14m^{2}n$.

Rewrite the product under a single fourth root: $\sqrt[4]{14m^{2}n}$.

This expression represents the simplified product of the original radicals using the product rule.

1:05m

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Struggling with Beginning & Intermediate Algebra?

Use the product rule to multiply the following.7m24⋅2n4\(\sqrt\)[4]{7m^2}\(\cdot\]\sqrt\)[4]{2n}

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Use the product rule to multiply the following.
$\sqrt[4]{7 m^{2}} \cdot \sqrt[4]{2 n}$