# simplify exponent and radical expressions

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1. Apply the rules of exponents to simply the following:

2. Write each of the following in a radical form: a) (3x)^(1/5)

3. express each of the following in exponent form.

4. simplify the radical expressions

5. For each of the following fractional terms, multiply the numerator and denominator by the conjugate of the denominator and simplify

6. Simplify with no negative exponents

7. Simplify

8. Factor the following where possible

9. Rewrite and simplify where possible

10. Supply the missing terms so that the fractions are equivalent

11. Reduce to lowest terms

12. Simplify

14. Combine and simplify

15. Simplify the complex fractions

16. The following expression arises in differential calculus:

a) Simplify the complex fractions

b) Determine the value of the simplified version when h = 0.

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The solution is comprised of detailed explanations of simplifying exponent, radical, and complex fractional expressions.

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Review of basic properties of exponent:

1. (a)

(b)

(c)

(d)

2. , so

(a) (b)

(c) (d)

(e)

3. (a)

(b)

(c)

(d)

4. (a)

(b)

5. (a)

(b)

6. (a)

(b)

(c)

(d)

(e) Using the distributive property of multiplication,

(f)

(g)

(h)

(i)

7. a)

So the quotient is (3x -2), the remainder is 2.

(b)

(c)

Therefore,

8. (a) Extract the GCF x3

(b) Extract the GCF x3(y+1)2:

(c) ...

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