Mathematics: PLS PLS PLS PLS PLS I GIVE ALL MAH POINTS

PLS PLS PLS PLS PLS I GIVE ALL MAH POINTS - id9237531, mcclendoncassandra

Ответ:

dakodahepps

10.02.2022

125 = 5³, and the given expression reduces to

$\left(\sqrt{125}\right)^{\frac13}\cdot\left(\sqrt[3]{125}\right)^{\frac12}=\left(125^{\frac12}\right)^{\frac13}\cdot\left(125^{\frac13}\right)^{\frac12}=125^{\frac16}\cdot125^{\frac16}=125^{\frac13}$

so it has a value of 5.

Now:

• the first choice is equivalent, since 625 = 25², so

$\dfrac{\sqrt[3]{625}}{5^{\frac13}}=\dfrac{25^{\frac23}}{5^{\frac13}}=\dfrac{5^{\frac43}}{5^{\frac13}}=5$

• the second choice is not equivalent, since

$5 \cdot 25^{\frac13} = 5 \cdot 5^{\frac23} = 5^{\frac43}$

• the third choice is also equivalent, since

$\dfrac{\left(\sqrt[4]{5}\right)^7}{125^{\frac14}}=\dfrac{5^{\frac74}}{5^{\frac34}}=5$

• the fourth choice is also equivalent, since

$\dfrac{5^{\frac12}\cdot25^{\frac13}}{\sqrt[6]{5}}=\dfrac{5^{\frac12}\cdot5^{\frac23}}{5^{\frac16}}=\dfrac{5^{\frac76}}{5^{\frac16}}=5$

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PLS PLS PLS PLS PLS I GIVE ALL MAH POINTS

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