3 years ago

What is 125^2/3 in simplest form? and What is \sqrt[5]({-245} ) ^{5} in simplest form?

1 answer:

5 0

${ 125 }^{ \frac { 2 }{ 3 } }\\ \\ ={ \left( { 125 }^{ \frac { 1 }{ 3 } } \right) }^{ 2 }\\ \\ ={ \left( \sqrt [ 3 ]{ 125 } \right) }^{ 2 }\\ \\ ={ 5 }^{ 2 }\\ \\ =25$

This is because:

${ a }^{ \frac { m }{ n } }\\ \\ =\sqrt [ n ]{ { a }^{ m } }$

Remember that:

5 x 5 x 5 = 125

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The two quadrilaterals below are similar. What is the length of EF?

damaskus [11]

EF = 15 cm.

Step-by-step explanation:

Step 1:

If the quadrilaterals, ABCD and EFGH are similar their side lengths will be of the same ratio throughout.

Comparing the quadrilaterals, we have AB and EF are similar, BC and FG are similar, CD and GH are similar, DA and HE are similar.

So the ratio of all these sides will be equal.

Step 2:

$\frac{AB}{EF} :\frac{BC}{FG} : \frac{CD}{GH} :\frac{DA}{HE} .$

Of these lengths, we only have the values for AB, BC, CD, DA, GH, HE and need to determine the length of EF. By substituting the known values the ratio becomes;

$\frac{5}{EF} :\frac{4}{12} :\frac{6}{18} .$