power, exponent, base, coefficient, simplify, evaluate

Interactive Component Under Construction

Exponent Laws

product law

x^mx^{n =} x^m+n

power of a product law

(xy)^m = x^m  y^m

power of a power law

(x^m)ⁿ =x^mn

quotient law

x^m/ x^{n =} x^m-n

power of a quotient law

(x/y)^m = x^m y^m

1/x^-m = x^m

Exponential Laws

Enter expressions that match the standard form shown on the right of each law.

power of a product law:    

power of a power law:  

quotient law: 

power of a quotient law: 

reciprocals: 

distributive property:  

(xy)^m = x^m  y^m

(x^m)ⁿ =x^mn

x^m ¸ x^{n =} x^m-n

(x/y)^m = x^m / y^m  = x^my^-m

1/x^-m = x^m

a(x+c) = ax +ac

= 9 + 81 = 90

^{Use BEDMAS to solve.}

= 9 - 81 = -72

^{Use BEDMAS to solve.}

= 3³⁺⁴ = 3⁷

^{Keep the common base, then add the exponents.}

= x²⁺⁶ = x⁸

= 2^2x3 =2⁶

^{Keep the base, then multiply  the exponents.}

= x^3x4 =3¹²

= (3x3x3)(bbb)

= 3³b³

^or

(3b)³ = (3¹b¹)³ = 3^1x3b^1x3 = 3³b³

= (xxxx)(yyyy)

= x⁴y⁴

^or

(xy)⁴ = (x¹y¹)⁴ = x^1x4y^1x4 = x⁴y⁴

= 3^5-2 = 3³

^{Keep the common base, then subtract the exponents.}

= x^6-2 = x⁴

= (3x3x3) /(bbb) = 27/b³

or

(3/b)³ = (3¹b¹)³ = 3^1x3/b^1x3)

= 3³/b³ = 27/b³

= (xxxx) /(yyyy) = x⁴/y⁴

or

(x/y)⁴ = (x¹/y¹)⁴ = x^1x4/y^1x4 = x⁴/y⁴