Question

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

Answer 1

Answer:

0.86603 is the answer of the question

Answer 2

Answer:

x = $\frac{3}{4}$

Step-by-step explanation:

Using the rule of exponents

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

Given

64$x^{\frac{1}{2} }$ = 27$x^{-\frac{5}{2} }$ ( divide both sides by $x^{-\frac{5}{2} }$ )

64 × $\frac{x^{\frac{1}{2} } }{x^{-\frac{5}{2} } }$ = 27

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

64 × $x^{\frac{1}{2}+\frac{5}{2} }$ = 27

64 x³ = 27 ( divide both sides by 64 )

x³ = $\frac{27}{64}$ ( take the cube root of both sides )

x = $\sqrt[3]{\frac{27}{64} }$ = $\frac{\sqrt[3]{27} }{\sqrt[3]{64} }$ = $\frac{3}{4}$