Answer/Discussion on Rational Exponents

College Algebra
Answer/Discussion to Practice Problems
Tutorial 5: Rational Exponents

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Answer/Discussion to 1a

*Rewrite exponent 1/2 as a square root

We are looking for the square root of 100 raised to the 1 power, which is the same as just saying the square root of 100.

If your exponent's numerator is 1, you are basically just looking for the root (the denominator's exponent).

Our answer is 10 since the square root of 100 is 10.

(return to problem 1a)

Answer/Discussion to 1b

*Rewrite exponent 2/3 as a cube root being squared

*Cube root of -1/64 = -1/4

In this problem we are looking for the cube root of -1/64 squared. Again, I think it is easier to do the root part first if possible. The numbers will be easier to work with.

The cube root of -1/64 is -4 and (-4) squared is 16.

(return to problem 1b)

Answer/Discussion to 2a

* Multiply like bases, add. exp

(return to problem 2a)

Answer/Discussion to 2b

*Raise a base to two exponents, mult. exp.

*Rewrite as recip. of base raised to pos. exp.

*Square root of 16 = 4

(return to problem 2b)

Answer/Discussion to 2c

* Divide like bases, sub. exp

*Rewrite as recip. of base raised to pos. exp.

(return to problem 2c)

Answer/Discussion to 3a

*Rewrite fourth root of x to the sixth power as x to the 6/4 power

*Simplify exponent
*Rewrite exponent 3/2 as a square root of x cubed

(return to problem 3a)

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