Rational Exponents (Grade 10)

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Rational Exponents

1. 
What is [math](3a^2)^3(4a^3)^0[/math] simplified?



2. 
Express each of the following with fractional exponents.

a. [math]root3(25^2)[/math]


b. [math]sqrt35[/math]



3. 
What is the exact value of each of the following radicals?

a.[math](2 3/4)^4[/math]


b. [math]((3^3)(3^2))^3[/math]


c. [math](4/20)^3[/math]


d. [math]sqrt(a^4b^6)[/math]


e. [math]root3(a^3)[/math]


f. [math]sqrt25[/math]



4. 
Which of the following is the simplified version of [math](6x^2-4x^5+2x^3)^3/(2x^4)[/math]
  1. [math](6x^6-4x^15+2x^9)/(2x^4)[/math]
  2. [math]108x^2-32x^11+4x^5[/math]
  3. [math](6x^5-4x^8+2x^6)/(2x^4)[/math]
  4. [math]108x-32x^4+4x^2[/math]
5. 
Express with positive exponents:

[math]root(4)(x^3)[/math]

[math]root(5)(x^-2)[/math]

[math](2root(3)(x^(2/3)))^4[/math]



6. 
Express the following expression in simplest radical form using only one radical sign.

[math]9^(1/2)*x^(3/2)*y^(5/4)[/math]



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