rule
For all numbers x and all integers m and n,
rulepower
Guy3

When you raise a power to a power,
you MULTIPLY
the exponents.

When in doubt, expand the terms (as shown at the right) to see what is happening.

pp1

pp2

4s

Examples: (numerical and algebraic applications)

1.  (52)5 = 510
Power raised to a power → multiply the exponents.		 2.  ((-10)3)5 = (-10)15
Negative number base: Power raised to a power → multiply the exponents.
3.  12haf
Fraction base: Power raised to a power → multiply the exponents.
 4.   6negg
One of the exponents is negative. Still follow the rule and multiply the exponents. Be careful of the sign. In this case a positive number times a negative number gives a negative number.
5. (a4)3 = a12
Variable base: Power raised to a power → multiply the exponents.
 6.  powex2
Numerical base with variable powers.
7.  powex4
Power raised to a power → multiply the exponents.
Negative exponents at work, but not for long.
8. powex3 
Result has a negative exponent. Do not leave the negative exponent as an answer.
9. (x2)a+2 = x2(a+2) = x2a+4
Power raised to a power → multiply the exponents.
The Distributive Property is also at work here.
 10. Negative exponent with quotient:10ex

 

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