Respuesta :
Answer:
Raising both sides to the second power will eliminate only one rational exponent
Step-by-step explanation:
we have
[tex](x+5)^{\frac{1}{2}}=(5-2x)^{\frac{1}{4}}[/tex]
If raising both sides to the 2nd power
[tex][(x+5)^{\frac{1}{2}}]^2=[(5-2x)^{\frac{1}{4}}]^2[/tex]
Remember the property of exponents
[tex](x^{m} )^{n} =x^{m*n}[/tex]
[tex]x^{\frac{m}{n}}=\sqrt[n]{x^m}[/tex]
so
Multiply the exponents
[tex](x+5)^{\frac{2}{2}}=(5-2x)^{\frac{2}{4}}[/tex]
Simplify
[tex](x+5)=(5-2x)^\frac{1}{2}[/tex]
[tex](x+5)=\sqrt{5-2x}[/tex]
therefore
Raising both sides to the second power will eliminate only one rational exponent
To eliminate both rational exponents, both sides must be raised to the fourth power
so
[tex][(x+5)^{\frac{1}{2}}]^4=[(5-2x)^{\frac{1}{4}}]^4[/tex]
[tex](x+5)^{\frac{4}{2}}=(5-2x)^{\frac{4}{4}}[/tex]
simplify
[tex](x+5)^2=(5-2x)[/tex]
Answer:
No. It will eliminate the rational exponent on the left side completely, but raising 1/4 to the 2nd power still leaves a rational exponent of 1/2 on the right side because 1/4 • 2 = 1/2.
Step-by-step explanation:
Edmentum
