MS Math Essentials Laws of Exponents

Simple

100

(6x^5)(3x)

(6x^5)(3x)

=6cdot3x^5x

=18x^6

200

7xyz(2x^2y)(3y^4z^5)

7xyz(2x^2y)(3y^4z^5)

=7cdot2cdot3x^1x^2y y y^4zz^5

=42x^3y^6z^6

300

(l^-1e^-2o^-3)^0/(f^ra^3n^-1k^2)^0

(l^-1e^-2o^-3)^0/(f^ra^3n^-1k^2)^0

=1/1=1

400

(crst)/(hi^2na)^-1

(crst)/(hi^2na)^-1

=(crst)cdot(hi^2na)

=crsthii na

=christ i na

500

(l^0oan^-1)/(n^-2(hg)^-1)

(l^0oan^-1)/(n^-2(hg)^-1)

=(1 cdot oan^(-1 - -2)hg)/n=oanhg

=hoang

Medium 1

100

(9a^7b(3a^6b^2))/(18a^5b^3)

(9a^7b(3a^6b^2))/(18a^5b^3)

=(27a^(7+6)b^(1+2))/(18a^5b^3)

=(3a^13b^3)/(2a^5b^3)

=(3a^(13-5))/2=(3a^8)/2

200

((3xyz)^4x^5y^2)/(9x^2y^2z)

((3xyz)^4x^5y^2)/(9x^2y^2z)

=(81x^4y^4z^4x^5y^2)/(9x^2y^2z)

=81/9x^(4+5-2)y^(4+2-2)z^(4-1)

=9x^7y^4z^3

300

(2^-2/3)^-1

(2^-2/3)^-1

=3/2^-2

=3cdot2^2=3cdot4=12

400

(-2)^0÷(-2)^2xx(-2)^3

(-2)^0÷(-2)^2xx(-2)^3

1/(-2)^2cdot(-2)^3/1

=(-2)^(3-2)=-2

500

((2x^-1y)/(x^-3y^-2))^-3

((2x^-1y)/(x^-3y^-2))^-3

=(2x^(-1-(-3))y^(1-(-2)))^-3

=(2x^2y^3)^-3

=1/(2x^2y^3)^3=1/(8x^6y^9)

Medium 2

100

(3x^3y^2)^3(2x^4y^2)^2

(3x^3y^2)^3(2x^4y^2)^2

=(27x^9y^6)(4x^8y^4)

=27cdot4x^(9+8)y^(6+4)

=108x^17y^10

200

((2x^3y^4)^5(3x^2y^7)^2)/(6x^5y^15)

((2x^3y^4)^5(3x^2y^7)^2)/(6x^5y^15)

=(2^5x^15y^20cdot3^2x^4y^14)/(2cdot3x^5y^15)

=2^4cdot3x^(15+4-5)y^(20+14-15)

=48x^14y^19

300

(-7/5)^-2

(-7/5)^-2

=(-5/7)^2

=25/49

400

7^-1xx7^-2÷7^-5

7^-1xx7^-2÷7^-5

=7^-3/7^-5

=7^(-3- -5)=7^2=49

500

(16x^3y^-5)/(4x^-6y^8)

(16x^3y^-5)/(4x^-6y^8)

=4x^(3-(-6))y^(-5-8)

=4x^9y^-13

=(4x^9)/y^13

Hard

100

(-2/5)^-2

(-2/5)^-2

=(-5/2)^2=25/4=6 1/4

200

(-3x^2)^2(2x^-2)^3

(-3x^2)^2(2x^-2)^3

=9x^4cdot8x^-6

=72x^(4-6)=72x^-2=72/x^2

300

(-2y^-3)^2(4z^6y^9)^-2

(-2y^-3)^2(4z^6y^9)^-2

=(4y^-6)/(4z^6y^9)^2

=4/(y^6cdot(16z^2y^18))

=1/(4z^12y^24)

400

(((-2/3)^2)^-2)^-1

(((-2/3)^2)^-2)^-1

=(-2/3)^(2cdot-2cdot-1)

=(-2/3)^4

=16/81

500

(2^(m+2)-2^m)/2^m

(2^(m+2)-2^m)/2^m

=(2^mcdot2^2-2^m)/2^m

=(2^m(4-1))/2^m=4-1=3