Question

Simplify : (5^-7 ÷ 5^-10 ) × 5^-5​

Answer 1

Given,

$(5^{-7} \div 5^{-10} )\times 5^{-5}$

The negative power in numerator becomes positive power when it goes to denominator.

So, $(\frac{1}{5^{7} } \div \frac{1}{5^{10} } )\times \frac{1}{5^{5} }$

$\frac{\frac{1}{5^{7} } }{\frac{1}{5^{10} } } \times \frac{1}{5^{5} }$

By using the formulas

$a^{m} \times a^{n} =a^{m+n} , \frac{a^{m} }{a^{n} } =a^{m-n}$

$={5^{10-7} } \times \frac{1}{5^{5} }$

$={5^{3} } \times \frac{1}{5^{5} }$

$={5^{3-5} }$

$={5^{-2} }\\=\frac{1}{5^{2} } \\=\frac{1}{25}$

Therefore the value is $\frac{1}{25}$

Answer 2

Answer:

$\frac{1}{25}$

Step-by-step explanation:

Given expression,

$(5^{-7}\div 5^{-10})\times5^{-5}$

we know, $x^{-n}=\frac{1}{x^{n} }$, $\frac{x^{m} }{x^{n} } =x^{m-n}$ and $x^{m}\times x^{n} =x^{m+n}$

Let us use the above formulas to simplify the given expression

$(5^{-7}\div 5^{-10})\times5^{-5}$

$=5^{-7+10}\times5^{-5}$    ( $\because \frac{x^{m} }{x^{n} } =x^{m-n}$)

$=5^{3} \times5^{-5}$      ( $\because x^{m}\times x^{n} =x^{m+n}$)

$=5^{3-5}$

$=5^{-2}$

$=\frac{1}{5^{2} }$    ($\because x^{-n}=\frac{1}{x^{n} }$)

$=\frac{1}{25}$

Hence, the answer is $\frac{1}{25}$.