Question

Calculate the value of x for the following equations. Show your working.​

Answer 1

0.86603 is the answer of the question

Answer 2

x =
`(3)/(4)`

Explanation:

Using the rule of exponents

`(a^(m) )/(a^(n) )` =
`a^((m-n))`

Given

64
`x^{(1)/(2) }` = 27
`x^{-(5)/(2) }` ( divide both sides by
`x^{-(5)/(2) }` )

64 ×
`\frac{x^{(1)/(2) } }{x^{-(5)/(2) } }` = 27

64 ×
`x^{(1)/(2)-(-(5)/(2)) }` = 27

64 ×
`x^{(1)/(2)+(5)/(2) }` = 27

64 x³ = 27 ( divide both sides by 64 )

x³ =
`(27)/(64)` ( take the cube root of both sides )

x =
`\sqrt[3]{(27)/(64) }` =
`\frac{\sqrt[3]{27} }{\sqrt[3]{64} }` =
`(3)/(4)`