Question

what is the value of (25)¾*(625)-¼​

Answer 1

Answer:

(5²)^3/4 * (5⁴)^-1/4

= 5^3/2 * 5^-1

= 5^(3/2-1)

= 5^1/2

= √5 (ans)

(Mark as brainlist)

Answer 2

Answer:

hey mate here is your answer:

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

we know that 5²=25 and 5⁴=625,

now, putting these stead of respective values:

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

Now,

multiple the powers with coinciding fraction:

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

Now we get;

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

From exponent's law:

$a {}^{ - 1} = \frac{1}{a}$

Apply this rule:

$= > (5) {}^{ \frac{3}{2} } \times \frac{1}{5}$

$= \frac{5 {}^{ \frac{3}{2} } }{5 {}^{1} }$

Also,

$\frac{a {}^{m} }{a {}^{n} } = a {}^{m - n}$

so:-

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

$= > 5 {}^{ \frac{1}{2} }$

but,

half to power equal to it's square root:

$= \sqrt{5}$