Question

simplyfy (25)3/2 x (625) -1/4 question

Answer 1

Answer:

$\red { (25)^{\frac{3}{2}} \times (625)^{\frac{-1}{4}}}\green { = 25 }$

Step-by-step explanation:

$\red { (25)^{\frac{3}{2}} \times (625)^{\frac{-1}{4}}}$

$= \left(5^{2}\right)^{\frac{3}{2}} \times \left(5^{4}\right)^{\frac{-1}{4}}$

$= 5^{2\times \frac{3}{2}} \times 5^{4\times \frac{-1}{4}}$

$\boxed { \pink { (a^{m})^{n} = a^{m\times n }}}$

$= 5^{3} \times 5^{-1}$

$= 5^{ 3-1}$

$\boxed { \pink { a^{m} \times a^{n} = a^{m+n}}}$

$= 5^{2}$

$\green { = 25 }$

Therefore.,

$\red { (25)^{\frac{3}{2}} \times (625)^{\frac{-1}{4}}}\green { = 25 }$

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