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

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Demonstration of a very slightly different method.

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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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