simplify (25)^5/2 *(729)^1/2 / (125)^2/3 *(27)^2/3 * (8)4/3
Answers
(5^2)^5/2 *(27^2)^1/2 / (5^3)^2/3 *(3^3)^2/3 * (2^3)4/3
{(5)^5*(27) }/ {(5)^2 *(3)^2 * (2)^4}
{(5)^3*(3) }/ { (2)^4} ( cancelling (5)^2 *(3)^2)
= 125*3/16
= 375/16 ans
Concept:
The representation of extremely big or extremely small numbers is described in an introduction to exponents. A value that is added to a number is called an exponent. Both exponents and powers have a relationship with one another.
7,350,000,000,000,000,000,000 kg is the moon's mass. However, the value is so great that it is difficult for us to read. Exponents were thus established in order to simplify the reading and writing of such large numbers.
(aⁿ)ˣ =aⁿˣ
a⁻ⁿ=1/aⁿ
Given:
(25)^5/2 *(729)^1/2 / (125)^2/3 *(27)^2/3 * (8)4/3
Find:
simplify (25)^5/2 *(729)^1/2 / (125)^2/3 *(27)^2/3 * (8)4/3
Solution:
(25)^5/2 *(729)^1/2 / (125)^2/3 *(27)^2/3 * (8)4/3
(5²)^5/2 X (27²)^1/2 / ((5³)^2/3 X (3³)^2/3 X (2³)^4/3)
{(5)⁵X(27) }/ {(5)² X(3)² X(2)⁴}
{(5)³ˣ³ }/ { (2)⁴} ( cancelling (5)² X(3)²)
= 125*3/16
= 375/16
Therefore, the answer is 375/16
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