Question

simplify the following
(a). (625) -1/4
​

Answer 1

Answer:

( 625)- ¼

625 = 5 * 5 * 5 * 5= (5)^4

((5)^4 )-¼

( cancel 4 )

5-¹

= 1/5

Answer 2

The answer is - $\frac{1}{5}$

GIVEN

Exponentiation 625⁻¹/⁴

TO FIND

Simplification of the given exponentiation.

SOLUTION:

We can simply solve the above problem as follows :

We know that exponentiation is a mathematical operation represented as bⁿ. Where b is the base and n is the exponent denoting multiplication of the base.

So, in the given problem

b= 625

n = -1/4

To simplify (625)⁻¹/⁴

we will first calculate the factors of 625

625 = 5×5×5×5

So, we can rewrite 625 as 5⁴

or,

625⁻¹/⁴ = (5⁴)⁻¹/⁴

Applying the exponent rules of the product - The exponents are multiplied

${5}^{4 \times \frac{ - 1}{4} }$

$= {5}^{ - 1}$

we know b⁻ⁿ = 1/bⁿ

So, 5⁻¹ = 1/5

Hence, The answer is -

$\frac{1}{5}$

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