[tex]zad.a ~~~~15^{4} \div 5^{4} =(\dfrac{15}{5} )^{4} =3^{4} =81\\\\zad.b ~~~~5^{4} \cdot 5^{2} =5^{4+2} =5^{6} =15~625\\\\zad.c ~~~~3^{4} \div 2^{3} =81\div 8= \dfrac{81}{8} =10\dfrac{1}{8} =10,125\\\\zad.d ~~~~3^{4} +3^{2} =81+9=90\\\\zad.e~~~~(3^{5} )^{4} =3^{5\cdot 4} =3^{20} =3~486~784~401\\\\zad.f ~~~~5^{10} \cdot 2^{10} =(5\cdot 2)^{10}=10^{10} =10~000~000~000\\\\zad.g~~~~70^{8} \div 7^{8} =(70\div 7)^{8} =10^{8} =100~000~000\\\\zad.h~~~~5^{0} -5^{2} =1-25=-24[/tex]
Korzystam ze wzorów:
[tex]x^{n} \cdot x^{m} =x^{n+m} \\\\x^{n} \div x^{m} =x^{n-m}\\\\x^{n} \div y^{n} =(x\div y)^{n} \\\\(x^{n} )^{m} =x^{n\cdot m} \\\\x^{n} \cdot y^{n} =(x\cdot y )^{n} \\\\x^{0} =1~~zal.~~x\neq 0[/tex]