Laws of Exponents 2

The following will provide additional practice. Click on the "Simplify" button. The solution will be given in a new window. Return to this window and click on the "Random" button. See if you can determine the solution before clicking the "Simplify" button again.

^ refers to an exponent. 3^3 refers to 3².

use / to represent divide and * to represent multiply.

use + and - for add and subtract.

any letter can be used as a variable.

Help

Click to enter an expression, then click the button. Try to calculate the answer mentally while the answer page loads. The Power Property rules in the chart above may be useful.

Power Property	Example	General Rule
quotient law	3⁵� 3²= (3x3x3x3x3)/(3x3) = 3^5-2 = 3³	x^m� x^{n =}x^m-n ^{Keep the common base, then subtract the exponents.}
	x⁶� x²= (xxxxxx)/(xx) = x^6-2 = x⁴
power of a quotient law	(3/b)³= (3/b)(3/b) (3/b) = (3x3x3) /(bbb) = 27/b³ or (3/b)³= (3¹b¹)³ = 3^1x3/b^1x3) = 3³/b³= 27/b³	(x/y)^m= x^m� y^m
	(x/y)⁴=(x/y) (x/y) (x/y) (x/y) = (xxxx) /(yyyy) = x⁴/y⁴ or (x/y)⁴= (x¹/y¹)⁴ = x^1x4/y^1x4= x⁴/y⁴
negative exponents	3^-4= (1/3)⁴= 1/3⁴	x^-m= (1/x)^m= 1/x^m
	x^-3= (1/x)³= 1/x³
	1/y^-4= (y/1)⁴= y⁴	1/x^-m= x^m

simplify and evaluate expressions involving powers.

Exponent Laws

The following will provide additional practice. Click on the "Simplify" button. The solution will be given in a new window. Change the bases and/or exponents in this new window. See if you can determine the solution before clicking the "Simplify" button again.