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Mathorio

Answer key

Rational Exponents

Show your work for each problem.

1.
What is ?
1. a)8
2. b)2
3. c)32
4. d)4
Answer: 4
because .
2.
Which expression is equivalent to ?
1. a)
2. b)
3. c)
4. d)
Answer:
, so . The root index becomes the denominator.
3.
What is ?
Answer: 2
because .
4.
What is ?
Answer: 3
because .
5.
Convert to radical form.
Answer: sqrt[5]{x^2}
1. What is the denominator of the exponent? 5
2. What is the numerator of the exponent? 2
3. Write the radical form: 5th root of x to what power? 2
6.
What is ?
1. a)6
2. b)4
3. c)2
4. d)16
Answer: 4
7.
What is ?
Answer: 4
because .
8.
What is ?
Answer: 27
because .
9.
Simplify .
Answer: x
1. When multiplying same bases, what do we do with exponents? add
2. What is ? 1
3. So 1
10.
Simplify .
Answer: x^(2/3)
1. When dividing same bases, what do we do with exponents? subtract
2. What is ? 4/6
3. Simplify : 2/3
11.
What is ?
1. a)
2. b)
3. c)
4. d)
Answer:
12.
What is ? Give your answer as a fraction.
Answer: 1/8
13.
Simplify .
Answer: 4x^4
1. Apply the exponent to each factor. What is ? 4
2. What is ? Use the power rule. x^4
3. Combine the results: 4x^4
14.
Simplify .
Answer: x
1. First add the exponents in the numerator. Convert to sixths: 4/6
2. Convert to sixths: 3/6
3. Add the numerator exponents: 7/6
4. Now subtract the denominator exponent: 6/6
5. So x
15.
Simplify .
1. a)
2. b)
3. c)
4. d)
Answer:
16.
Evaluate .
Answer: 32
1. Express 64 as a power of 2. 6
2. Rewrite: 5
3. What is ? 32