# How do you simplify #(-64)^(-2/3)#?

See a solution process below:

First, rewrite the expression as:

Next, use this rule of exponents to separate the exponents:

Then, use this rule of exponents to eliminate the negative exponent:

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To simplify ((-64)^{-\frac{2}{3}}), you first take the reciprocal of the base and then apply the exponent. So, ((-64)^{-\frac{2}{3}} = \frac{1}{(-64)^{\frac{2}{3}}}).

To simplify ((-64)^{\frac{2}{3}}), first find the cube root of the base ((-64)), which is (-4) because ((-4)^3 = -64). Then, raise (-4) to the power of (2) to get (16).

Therefore, ((-64)^{\frac{2}{3}} = 16).

Now, substitute (16) back into the expression (\frac{1}{(-64)^{\frac{2}{3}}}):

(\frac{1}{16}).

So, ((-64)^{-\frac{2}{3}}) simplifies to (\frac{1}{16}).

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When evaluating a one-sided 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 one-sided 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 one-sided 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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