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How do you simplify #13^4 / sqrt(13^10)#?

Answer 1

Cameron Arnold

#13^4/(sqrt(13^10))=1/13#

#13^4/(sqrt(13^10)#

= #13^4/(13^10)^(1/2)#

= #13^4/(13^((10xx1/2)))#

= #13^4/13^5#

= #(13xx13xx13xx13)/(13xx13xx13xx13xx13)#

= #1/13#

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Answer 2

Nova Allen

Demonstration of a very slightly different method.

#1/13#

Another way of writing #sqrt(13^10)" "# is #" "13^(10/2)#

But we have #1/sqrt(13^10)" "# which is the same as #13^(-10/2)#

So #" "13^4/sqrt(13^10) = 13^4xx10^(-10/2)#

But #10/2=5# giving

#13^4xx13^(-5)#

#13^(4-5)= 13^(-1) = 1/13#

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Answer 3

Gabriel Agustin

To simplify ( \frac{13^4}{\sqrt{13^{10}}} ), we first rewrite the expression using exponent properties.

[ \frac{13^4}{\sqrt{13^{10}}} = \frac{13^4}{(13^{10})^{1/2}} ]

Now, we apply the properties of exponents. When a power is raised to another power, we multiply the exponents.

[ = 13^4 \times 13^{10 \times \frac{1}{2}} ]

[ = 13^4 \times 13^5 ]

Now, when multiplying two numbers with the same base, we add the exponents.

[ = 13^{4 + 5} ]

[ = 13^9 ]

So, ( \frac{13^4}{\sqrt{13^{10}}} ) simplifies to ( 13^9 ).

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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.