Apply the power laws to simplify the following expressions:
32⋅31
For this task you need the following basic knowledge: Power Laws
Use the power law ax⋅ay=ax+y with x=2,y=1,a=3.
Conclude the exponent.
42⋅49⋅4−12
First apply the power laws to 42⋅49.
Now apply the power law to 411⋅4−12.
The term can be simplified even further by using the rule of the negative exponent, that is a−1=1a.
48⋅2−3⋅25⋅59
Apply the power law ax⋅ay=ax+y to 2−3⋅25.
Write 22=2⋅2=4=41.
Apply the power law ax⋅ay=ax+y to 48⋅41.
Apply the power law ax⋅bx=(a⋅b)x.
(77)7
Apply the power law (ax)y=ax⋅y.
Conclude the exponent
929−3:35
Apply the power law axay=ax−y to 929−3.
Summarize the exponent of 9.
Write a:b=ab.
Use the power law axbx=(ab)x.
Conclude the base.
26226813−3133
Use the power law axay=ax−y with base a=26.
Use the power law axay=ax−y with base a=13.