Solving powers requires an understanding of multiplication rules. A power, or exponent, is a shortcut to indicate a number should be multiplied by itself. The number being multiplied is referred to as the "base." The exponent is located to the right of the base in superscript or with the ^ symbol appearing before it.
Determine if the base is negative or positive.
Check for parenthesis placement, especially when working with a negative base. Keep in mind (-3)^4 is different from -3^4.
For a positive base, multiply the number as indicated by the exponent. For 5^3, multiple 5_5_5 to arrive at your answer of 125.
For a base whose negative sign is contained in the parenthesis, keep the negative symbol in front of each act of multiplication. For example, (-3)^4 would be multiplied as (-3)(-3)(-3)*(-3), to arrive at your answer of 81.
For exponents whose negative sign is without parenthesis, save the negative symbol until after you have finished multiplying the base. For example, -3^4 would be multiplied as -(3)(3)(3)(3), to arrive at your answer of -81.
If you have an equation consisting of two exponents with the same base, you can add the exponents together for simplification. For example, 2^3_2_4 can be converted to 2^7. Then, you can solve the equation as usual.
Remember that, as with all algebraic functions, anything inside parenthesis must be dealt with first.