Multiplication
What is the rule for multiplying indices?
a^mxxa^n=a^(m+n)
What is the rule for dividing indices?
a^m/a^n=a^(m-n)
What is the rule when there is a power outside a bracket?
(a^m)^n=a^(m*n)
What is the rule when a letter or number is raised to the power of zero?
a^0=1
What is the rule when a base has a negative power?
a^-n=1/a^n
Simplify:
n^3xxn^4
=n^(3+4)
=n^7
Simplify:
y^9/y^4
=y^(9-4)
=y^5
Simplify:
(z^4)^7
=z^(4xx7)
=z^28
Simplify:
5^0
=1
Simplify:
7^-2
=1/7^2
=1/49
Simplify:
a^8b^3xxa^4b^7
=a^(8+4)b^(3+7)
=a^12b^10
Simplify:
(u^12v^8)/(u^3v)
=u^(12-3)xxv^(8-1)
=u^9v^7
Simplify:
(3p)^3
=3^3xxp^(1xx3)
=27p^3
Simplify:
x^0
=1
Write with a positive index.
n^-3
1/n^3
Simplify:
5p^2xx3p^4
=5xx3xxp^(2+4)
=15p^6
Simplify:
(21c^9)/(3c^5)
=21/3xxc^(9-5)
=7c^4
Simplify:
(2x^5)^4
=2^4xxx^(5xx4)
=16x^20
Simplify:
2k^0
=2xxk^0
=2xx1
=2
Write with a negative index.
1/c^2
c^-2
Simplify:
1/2k^6xx8k
=1/2xx8xxk^(6+1)
=4k^7
Simplify:
(-42e^8f^12)/(7e^2f^5)
=-42/7xxe^(8-2)xxf^(12-5)
=-6e^6f^7
Simplify:
(-2j^4k^9)^3
-2^3xxj^(4xx3)xxk^(9xx3)
=-8j^12k^27
Simplify:
p^0q
=p^0xxq
=1xxq
=q
Simplify
2z^9xx9z^-2
=2xx9xxz^(9+ - 2)
=18z^7