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How do you evaluate #\sqrt[9](x-3)\cdot \sqrt[9]((x-3)^{7})#?

Answer 1

Julia Adams

See a solution process below:

First, evaluate the #sqrt(9)# terms:

#3(x - 3) * 3((x - 3)^7)#

Next, rewrite the expression as:

#3 * 3((x - 3) * (x - 3)^7)#

#9((x - 3)^1 * (x - 3)^7)#

#9(x - 3)^(1 + 7)#

#9(x - 3)^8#

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Answer 2

Kennedy Adams

To evaluate (\sqrt[9]{(x-3)} \cdot \sqrt[9]{(x-3)^7}), you can simplify by combining the two radical terms:

(\sqrt[9]{(x-3)} \cdot \sqrt[9]{(x-3)^7} = \sqrt[9]{(x-3) \cdot (x-3)^7})

Using the properties of exponents, we can combine the terms inside the radical:

(\sqrt[9]{(x-3) \cdot (x-3)^7} = \sqrt[9]{(x-3)^8})

Now, apply the exponent rule for roots:

(\sqrt[9]{(x-3)^8} = (x-3)^{\frac{8}{9}})

Therefore, the simplified expression is ((x-3)^{\frac{8}{9}}).

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Answer from HIX Tutor

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.