Powers

Power facts

 * When multiplying powers of the same number, add the powers:
 * $$x^a \times x^b = x^{a+b}$$


 * When dividing powers of the same number, subtract the powers:
 * $$x^a \div x^b = x^{a-b}$$


 * $$\frac {x^a} {x^b} = x^{a-b}$$


 * Powers outside brackets multiply by powers inside the brackets:
 * $$(x^a)^b = x^{a \times b}$$


 * Any number to the power of 0 is equal to 1:
 * $$x^0 = 1$$


 * Negative powers are reciprocals:
 * $$x^{-a} = \frac {1} {x^a}$$


 * Any number to the power of one half is equal to the square root of that number:
 * $$x^{\frac {1} {2}} = \sqrt x$$


 * With fractional powers, the numerator is a power and the denominator is a root:
 * $$x^{\frac {a} {b}} = (\sqrt [b] x)^a$$