Answer:
a) 4 to the 14th power
b) 12 to the 9th power
c) 5 to the 7th power
d) 7 to the 3rd power
Step-by-step explanation:
a) [tex]4^{6}[/tex] · [tex]4^{8}[/tex] equals 4 to the 14th power.
Using the Product Rule of Exponents:
[tex]a^{m} a^{n} = a^{m+n}[/tex]
You could add the exponents since they have the same base.
b) [tex]12^{6}[/tex] · [tex]12^{3}[/tex] equals 12 to the 9th power.
Same Product Rule applies as we did in problem a).
c) [tex]\frac{5^{10} }{5^{3} }[/tex] equals 5 to the 7th power.
Using the Quotient Rule of Exponents:
[tex]\frac{a^{m} }{a^{n} } = a^{m - n}[/tex]
You'll have to subtract the exponents since they have the same base.
[tex]\frac{5^{10} }{5^{3} } = 5^{10 - 3} = 5^{7}[/tex]
d) [tex]\frac{7^{6} }{7^{3} }[/tex] equals 7 to the 3rd power.
Same Quotient Rule applies as we did in problem c).
[tex]\frac{7^{6} }{7^{3} } = 7^{6 - 3} = 7^{3}[/tex]
