(x+5)1/2=(5-2x)1/4 This equation has two different rational exponents, 1/2 and 1/4 . The inverse powers for these two rational exponents would be 2 and 4, respectively. Will raising both sides to the 2nd power eliminate both rational exponents? Explain.

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]

90v00x

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:

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