Exponential notation and algebraic laws for powers, including a0=1, negative exponents, multiplying and dividing powers with the same base, exponents of products and quotients and powers of powers (am)n=amn.
Exponential expressions are a shortcut for writing the multiplication of a number by itself many times:
Here a is called the base and n the exponent. We say that a is raised to the nth power.
Note that a1=a, since we have 1×a=a.
Any number raised to the power zero is
And since any number multiplied by 0 is 0:
When n=0, we have 00, which is technically undefined, but in most contexts is defined to be
When multiplying exponentials with the same base, the following rule applies:
An exponential can be the base of another exponential:
In general,
When exponentials with the same power are being multiplied or divided, the bases can be combined:
If two exponentials in the same positive base are equal, their exponents must be equal:
Exponentials can also appear in equations with one or more unknown:
Now we can equate the exponents:
Nice work completing Exponentiation and integer exponent laws, here's a quick recap of what we covered:
Exercises checked off
Exponential notation and algebraic laws for powers, including a0=1, negative exponents, multiplying and dividing powers with the same base, exponents of products and quotients and powers of powers (am)n=amn.
Exponential expressions are a shortcut for writing the multiplication of a number by itself many times:
Here a is called the base and n the exponent. We say that a is raised to the nth power.
Note that a1=a, since we have 1×a=a.
Any number raised to the power zero is
And since any number multiplied by 0 is 0:
When n=0, we have 00, which is technically undefined, but in most contexts is defined to be
When multiplying exponentials with the same base, the following rule applies:
An exponential can be the base of another exponential:
In general,
When exponentials with the same power are being multiplied or divided, the bases can be combined:
If two exponentials in the same positive base are equal, their exponents must be equal:
Exponentials can also appear in equations with one or more unknown:
Now we can equate the exponents:
Nice work completing Exponentiation and integer exponent laws, here's a quick recap of what we covered:
Exercises checked off