Step-by-step explanation:
the answer is 10 . hope it helps
Solve ⇒
To solve this we must apply laws of exponents. First of all we must simplify 4 to 2².
⇒
Now we will apply this law of exponent ⇒
Now we shall apply this law of exponent ⇒
Now we shall apply these laws of exponents ⇒ and
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Answers & Comments
Step-by-step explanation:
the answer is 10 . hope it helps
Question
Solve ⇒![\sf (\dfrac{2}{5})^{-3} \times (\dfrac{5}{4})^{-2} \sf (\dfrac{2}{5})^{-3} \times (\dfrac{5}{4})^{-2}](https://tex.z-dn.net/?f=%5Csf%20%28%5Cdfrac%7B2%7D%7B5%7D%29%5E%7B-3%7D%20%5Ctimes%20%28%5Cdfrac%7B5%7D%7B4%7D%29%5E%7B-2%7D)
Answer
To solve this we must apply laws of exponents. First of all we must simplify 4 to 2².
⇒![\sf (\dfrac{2}{5})^{-3} \times (\dfrac{5}{4})^{-2} \sf (\dfrac{2}{5})^{-3} \times (\dfrac{5}{4})^{-2}](https://tex.z-dn.net/?f=%5Csf%20%28%5Cdfrac%7B2%7D%7B5%7D%29%5E%7B-3%7D%20%5Ctimes%20%28%5Cdfrac%7B5%7D%7B4%7D%29%5E%7B-2%7D)
⇒![\sf (\dfrac{2}{5})^{-3} \times (\dfrac{5}{2^{2}})^{-2} \sf (\dfrac{2}{5})^{-3} \times (\dfrac{5}{2^{2}})^{-2}](https://tex.z-dn.net/?f=%5Csf%20%28%5Cdfrac%7B2%7D%7B5%7D%29%5E%7B-3%7D%20%5Ctimes%20%28%5Cdfrac%7B5%7D%7B2%5E%7B2%7D%7D%29%5E%7B-2%7D)
Now we will apply this law of exponent ⇒![a^{-m}=\frac{1}{a^{m}} a^{-m}=\frac{1}{a^{m}}](https://tex.z-dn.net/?f=a%5E%7B-m%7D%3D%5Cfrac%7B1%7D%7Ba%5E%7Bm%7D%7D)
⇒![\sf (\dfrac{2}{5})^{-3} \times (\dfrac{5}{2^{2}})^{-2} \sf (\dfrac{2}{5})^{-3} \times (\dfrac{5}{2^{2}})^{-2}](https://tex.z-dn.net/?f=%5Csf%20%28%5Cdfrac%7B2%7D%7B5%7D%29%5E%7B-3%7D%20%5Ctimes%20%28%5Cdfrac%7B5%7D%7B2%5E%7B2%7D%7D%29%5E%7B-2%7D)
⇒![\sf (\dfrac{5}{2})^{3} \times (\dfrac{2^{2}}{5})^{2} \sf (\dfrac{5}{2})^{3} \times (\dfrac{2^{2}}{5})^{2}](https://tex.z-dn.net/?f=%5Csf%20%28%5Cdfrac%7B5%7D%7B2%7D%29%5E%7B3%7D%20%5Ctimes%20%28%5Cdfrac%7B2%5E%7B2%7D%7D%7B5%7D%29%5E%7B2%7D)
Now we shall apply this law of exponent ⇒![(a^{m})^{n}=a^{m\times n} (a^{m})^{n}=a^{m\times n}](https://tex.z-dn.net/?f=%28a%5E%7Bm%7D%29%5E%7Bn%7D%3Da%5E%7Bm%5Ctimes%20n%7D)
⇒![\sf (\dfrac{5}{2})^{3} \times (\dfrac{2^{2}}{5})^{2} \sf (\dfrac{5}{2})^{3} \times (\dfrac{2^{2}}{5})^{2}](https://tex.z-dn.net/?f=%5Csf%20%28%5Cdfrac%7B5%7D%7B2%7D%29%5E%7B3%7D%20%5Ctimes%20%28%5Cdfrac%7B2%5E%7B2%7D%7D%7B5%7D%29%5E%7B2%7D)
⇒![\sf (\dfrac{5}{2})^{3} \times (\dfrac{2^{4}}{5^{2}}) \sf (\dfrac{5}{2})^{3} \times (\dfrac{2^{4}}{5^{2}})](https://tex.z-dn.net/?f=%5Csf%20%28%5Cdfrac%7B5%7D%7B2%7D%29%5E%7B3%7D%20%5Ctimes%20%28%5Cdfrac%7B2%5E%7B4%7D%7D%7B5%5E%7B2%7D%7D%29)
Now we will apply this law of exponent ⇒![(\frac{a}{b})^{m} = \frac{a^{m}}{b^{m}} (\frac{a}{b})^{m} = \frac{a^{m}}{b^{m}}](https://tex.z-dn.net/?f=%28%5Cfrac%7Ba%7D%7Bb%7D%29%5E%7Bm%7D%20%3D%20%5Cfrac%7Ba%5E%7Bm%7D%7D%7Bb%5E%7Bm%7D%7D)
⇒![\sf (\dfrac{5}{2})^{3} \times (\dfrac{2^{4}}{5^{2}}) \sf (\dfrac{5}{2})^{3} \times (\dfrac{2^{4}}{5^{2}})](https://tex.z-dn.net/?f=%5Csf%20%28%5Cdfrac%7B5%7D%7B2%7D%29%5E%7B3%7D%20%5Ctimes%20%28%5Cdfrac%7B2%5E%7B4%7D%7D%7B5%5E%7B2%7D%7D%29)
⇒![\sf \dfrac{5^{3}}{2^{3}} \times \dfrac{2^{4}}{5^{2}} \sf \dfrac{5^{3}}{2^{3}} \times \dfrac{2^{4}}{5^{2}}](https://tex.z-dn.net/?f=%5Csf%20%5Cdfrac%7B5%5E%7B3%7D%7D%7B2%5E%7B3%7D%7D%20%5Ctimes%20%5Cdfrac%7B2%5E%7B4%7D%7D%7B5%5E%7B2%7D%7D)
Now we shall apply these laws of exponents ⇒
and ![a^{m}\div a^{n} = a^{m-n} a^{m}\div a^{n} = a^{m-n}](https://tex.z-dn.net/?f=a%5E%7Bm%7D%5Cdiv%20a%5E%7Bn%7D%20%3D%20a%5E%7Bm-n%7D)
⇒![\sf \dfrac{5^{3}}{2^{3}} \times \dfrac{2^{4}}{5^{2}} \sf \dfrac{5^{3}}{2^{3}} \times \dfrac{2^{4}}{5^{2}}](https://tex.z-dn.net/?f=%5Csf%20%5Cdfrac%7B5%5E%7B3%7D%7D%7B2%5E%7B3%7D%7D%20%5Ctimes%20%5Cdfrac%7B2%5E%7B4%7D%7D%7B5%5E%7B2%7D%7D)
⇒![\sf 5^{3-2}\times 2^{4-3} \sf 5^{3-2}\times 2^{4-3}](https://tex.z-dn.net/?f=%5Csf%205%5E%7B3-2%7D%5Ctimes%202%5E%7B4-3%7D)
⇒![\sf 5^{1}\times 2^{1} \sf 5^{1}\times 2^{1}](https://tex.z-dn.net/?f=%5Csf%205%5E%7B1%7D%5Ctimes%202%5E%7B1%7D)
⇒![\sf 10 \sf 10](https://tex.z-dn.net/?f=%5Csf%2010)