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(a) Write down the value of $125^{rac{1}{3}}$ - Edexcel - A-Level Maths Pure - Question 3 - 2009 - Paper 1

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$(a)-Write-down-the-value-of-$125^{-rac{1}{3}}$-Edexcel-A-Level Maths Pure-Question 3-2009-Paper 1.png$

(a) Write down the value of $125^{rac{1}{3}}$. (b) Find the value of $125^{-rac{2}{3}}$.

Worked Solution & Example Answer:(a) Write down the value of $125^{rac{1}{3}}$ - Edexcel - A-Level Maths Pure - Question 3 - 2009 - Paper 1

Step 1

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Answer

To find the value of $125^{ rac{1}{3}}$ , we need to determine the cube root of 125. Since $125 = 5^3$ , we have:

$125^{ rac{1}{3}} = (5^3)^{ rac{1}{3}} = 5.$

Thus, the value is 5.

Step 2

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Answer

To find the value of $125^{- rac{2}{3}}$ , we first convert it to a positive exponent:

$125^{- rac{2}{3}} = rac{1}{125^{ rac{2}{3}}}.$

Next, we find $125^{ rac{2}{3}}$ :

$125^{ rac{2}{3}} = (125^{ rac{1}{3}})^2 = 5^2 = 25.$

Thus, we have:

$125^{- rac{2}{3}} = rac{1}{25}.$

This means the value is $rac{1}{25}$ .

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