Question

(3^-7 ÷ 3^-10) 3^-5​

Answer 1

Answer:

$\frac{1}{3}$²

Step-by-step explanation:

Answer 2

To Find:

$\frac{3^{-7} }{3^{-10} })3^{-5}$

Solution:

Using the formula,

       $\frac{a^{m} }{a^{n} } = a^{m-n}$

    $\frac{3^{-7} }{3^{-10} } = 3^{-7-(-10)}$

            = $3^{3}$

      $(3^{3})(3^{-5})$

⇒ $(3^{3})(3^{-5}) = 3^{(3+ (-5)}$                                [∵$(a^{m})(a^{n}) = a^{m+n}$]

                  = $3^{-2}$

Now, the exponent is negative so we need to convert this answer to the positive exponent.

     $a^{-m = \frac{1}{a^{m} } }$

    $3^{-2} = \frac{1}{3^{2} }$

           = $\frac{1}{3^{2} }$