Respuesta :
Answer:
[tex]x=2^{\frac{2}{3}}[/tex]
Step-by-step explanation:
1) Add 8 to both sides.
[tex]2x^3=8[/tex]
2) Divide both sides by 2.
[tex]x^3=\frac{8}{2}[/tex]
3) Simplify [tex]\frac{8}{2}[/tex] to 4.
[tex]x^3=4[/tex]
4) Take the cube root of both sides.
[tex]x=\sqrt[3]{4}[/tex]
5) Rewrite 4 as 2².
[tex]x=\sqrt[3]{2^2}[/tex]
6) Use this rule: [tex]{({x}^{a})}^{b}={x}^{ab}[/tex].
[tex]x=2^{\frac{2}{3}}[/tex]
Decimal Form: 1.587401
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Check the answer:
[tex]2x^3-8=0[/tex]
1) Let [tex]x=2^\frac{2}{3}[/tex].
[tex]2(2^{\frac{2}{3} })-8=0[/tex]
2) Use this rule: [tex](x^a)^b=x^{ab}[/tex].
[tex]2\times2^{\frac{2\times3}{3} } -8=0[/tex]
3) Simplify 2 * 3 to 6.
[tex]2\times2^{\frac{6}{3} } - 8 =0[/tex]
4) Simplify 6/3 to 2.
[tex]2\times2^2-8=0[/tex]
5) Use Product Rule: [tex]x^ax^b=x^{a+b}[/tex].
[tex]2^3-8=0[/tex]
6) Simplify 2^3 to 8.
8 - 8 = 0
7) Simplify 8 - 8 to 0.
0 = 0
Thank you,
Eddie
