Question

Simplify 6 to the negative 3rd power over 6 to the 5th. 68 6−2 1 over 6 to the 8th power 1 over 6 to the 2nd power

Answer 1

Answer:

The simplified expression is given by:

                 1 over 6 to the 8th power.

                      $\dfrac{1}{6^8}$

Step-by-step explanation:

We are asked to simplify the expression:

6 to the negative 3rd power over 6 to the 5th power.

which is mathematically written as:

$\dfrac{6^{-3}}{6^5}$

Now, we know that:

$\dfrac{a^m}{a^n}=\dfrac{1}{a^{n-m}}$

Here,

$m=-3\ and\ n=5$

Hence, we get:

$\dfrac{6^{-3}}{6^5}=\dfrac{1}{6^{5-(-3)}}$

i.e.

$\dfrac{6^{-3}}{6^5}=\dfrac{1}{6^{5+3}}$

Hence, we get the simplified expression as follows:

$\dfrac{6^{-3}}{6^5}=\dfrac{1}{6^8}$

Answer 2

Answer:

$\dfrac{1}{6^8}$

Step-by-step explanation:

$\dfrac{6^{-3}}{6^5}=\dfrac{1}{6^{5+3}}=\dfrac{1}{6^8}$

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The applicable rules of exponents are ...

$a^{-b}=\dfrac{1}{a^b}\\\\a^b\times a^c=a^{b+c}$