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SVEN [57.7K]
3 years ago
11

A and b are positive integers and a–b = 3. Evaluate the following: 125^(1/3a)/25^(1/2b)

Mathematics
2 answers:
Snezhnost [94]3 years ago
5 0

Answer:

125

Step-by-step explanation:

\dfrac{125^{\frac{1}{3}a}}{25^{\frac{1}{2}b}} =

= \dfrac{(5^3)^{\frac{1}{3}a}}{(5^2)^{\frac{1}{2}b}}

= \dfrac{5^{3 \times \frac{1}{3}a} }{5^{2 \times \frac{1}{2}b}}

= \dfrac{5^{\frac{3}{3}a}}{5^{\frac{2}{2}b}}

= \dfrac{5^a}{5^b}

= 5^{a - b}

= 5^3

= 125

gizmo_the_mogwai [7]3 years ago
4 0

Value of \dfrac{125^{1/3a}}{25^{1/2b}} is  \dfrac{1}{125^{(\frac{1}{ab})}} .

<u>Step-by-step explanation:</u>

Here we have , a-b=3 . We need to evaluate : 125^(1/3a)/25^(1/2b) or ,

\dfrac{125^{1/3a}}{25^{1/2b}} . Let's find out:

⇒ \dfrac{125^{1/3a}}{25^{1/2b}}

⇒ \dfrac{5^3(^{1/3a})}{5^2(^{1/2b})}

⇒ \dfrac{5(^{3/3a})}{5(^{3/2b})}

⇒ 5^{(\frac{1}{a}-\frac{1}{b})} = 5^{(\frac{b-a}{ab})}

⇒ 5^{(\frac{-3}{ab})}

⇒ \dfrac{1}{125^{(\frac{1}{ab})}}

Therefore, Value of \dfrac{125^{1/3a}}{25^{1/2b}} is  \dfrac{1}{125^{(\frac{1}{ab})}} .

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