Answer:
Step-by-step explanation:
Exponent Law:
[tex]\sf \left(\dfrac{a}{b} \right)^{m}=\dfrac{a^{m}}{b^n}\\\\a^m *a^n =a^{m+n}\\\\\dfrac{a^{m}}{a^n}=a^{m-n}[/tex]
In exponent law, in multiplication, if bases are same add the powers and in division, if the bases are same, subtract the powers.
3)
[tex]\sf \left(\dfrac{7}{3} \right)^{-2}*\left(\dfrac{1}{7}\right)^{5}*\left(\dfrac{3}{5} \right)^{2}=\dfrac{7^{-2}}{3^{-2}}*\dfrac{1}{7^5}*\dfrac{3^2}{5^{2}}[/tex]
[tex]= \dfrac{7^{-2-5}*3^{2-[-2]}}{5^2}\\\\= \dfrac{7^{-7}*3^{2+2}}{5^{2}}\\\\=\dfrac{3^{4}}{7^7*5^{2}}[/tex]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~```
4)
[tex]\sf \left(\dfrac{2}{5}\right)^3*\left(\dfrac{2}{3}\right)^{-2}*\left(\dfrac{3}{5}\right)^2=\dfrac{2^3}{5^3}*\dfrac{2^{-2}}{3^{-2}}*\dfrac{3^2}{5^2}[/tex]
[tex]= \dfrac{2^{3-2}*3^{2-[-2]}}{5^{3+2}}\\\\=\dfrac{2*3^{2+2}}{5^{5}}\\\\=\dfrac{2*3^4}{5^5}[/tex]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`````
5)
[tex]\sf \left(\dfrac{3}{10}\right)^4*\left(\dfrac{10}{15}\right)^{2}*\left(\dfrac{5}{3}\right)^{3}=\left(\dfrac{3}{2*5}\right)^4*\left(\dfrac{2*5}{3*5}\right)^{2}*\left(\dfrac{5}{3}\right)^{3}[/tex]
[tex]=\left(\dfrac{3}{2*5}\right)^4*\left(\dfrac{2}{3}\right)^{2}*\left(\dfrac{5}{3}\right)^{3}\\\\=\dfrac{3^4}{2^4*5^4}*\dfrac{2^2}{3^2}*\dfrac{5^3}{3^3}\\\\=3^{4-2-3}*2^{2-4}*5^{3-4}\\\\=3^{-1}*2^{-2}*5^{-1}\\\\=\dfrac{1}{3*2^{2}*5}\\\\=\dfrac{1}{3*4*5}\\\\=\dfrac{1}{60}[/tex]
