How do you evaluate #( \frac { 8} { 27} ) ^ {  \frac { 2} { 3} }# without using a calculator?
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See a solution process below:
First, rewrite this expression as:
We can rewrite this using this rule for exponents:
We can now write this in radical form using this rule:
We can now use this rule for dividing radicals to evaluate the radical:
Yet again, we can rewrite this as:
Now, using these rules of exponents, yes, we can rewrite this again and then evaluate:
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To evaluate ( \left(\frac{8}{27}\right)^{\frac{2}{3}} ) without using a calculator, follow these steps:

Rewrite ( \frac{8}{27} ) as ( \left(\frac{2}{3}\right)^3 ), since ( 2^3 = 8 ) and ( 3^3 = 27 ).

Raise ( \left(\frac{2}{3}\right)^3 ) to the power of ( \frac{2}{3} ), which is equivalent to taking the reciprocal and then raising it to the power of ( \frac{2}{3} ).

The reciprocal of ( \left(\frac{2}{3}\right)^3 ) is ( \left(\frac{3}{2}\right)^3 ).

Raise ( \left(\frac{3}{2}\right)^3 ) to the power of ( \frac{2}{3} ).

Cube both the numerator and denominator separately: ( 3^2 = 9 ) and ( 2^2 = 4 ).

The result is ( \left(\frac{3}{2}\right)^2 = \frac{9}{4} ).
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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