Question

5 power minus 2 into 10 power minus 4 by 2 power minus 5 into 5 power minus 6

Answer 1

Answer:

Write this question in mathematical form!!!!

Answer 2

$\dfrac{5^{-2}\times 10^{-4}}{2^{-5}\times 5^{-6}}=2$

Step-by-step explanation:

Given expression, $\dfrac{5^{-2}\times 10^{-4}}{2^{-5}\times 5^{-6}}$

Step 1. Use the formula $a^{-1}=\dfrac{1}{a}$

$=\dfrac{2^{5}\times 5^{6}}{5^{2}\times 10^{4}}$

Step 2. Use the formula $(a\times b)^{m}=a^{m}\times b^{m}$

$=\dfrac{2^{5}\times 5^{6}}{5^{2}\times (2\times 5)^{4}}$

$=\dfrac{2^{5}\times 5^{6}}{5^{2}\times 2^{4}\times 5^{4}}$

Step 3. Use the formula $\dfrac{a^{m}}{a^{n}}=a^{m-n}$ and $a^{m}\times a^{n}=a^{m+n}$

$=\dfrac{2^{5}\times 5^{6}}{5^{2+4}\times 2^{4}}$

$=\dfrac{2^{5}\times 5^{6}}{5^{6}\times 2^{4}}$

$=2^{5-4}\times 5^{6-6}$

$=2^{1}\times 5^{0}$

Step 4. Use $a^{0}=1$ where $a\neq 0$ and $a^{1}=a$

$=2\times 1$

$=2$

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