Grade 8 Mathematics
Exponents are a shorthand for repeated multiplication. The LAWS OF EXPONENTS help us simplify expressions with the same base!
x^n means: multiply x by itself n times
When multiplying same bases, ADD the exponents!
Examples:
x^3 times x^4 = x^(3+4) = x^7
2^5 times 2^3 = 2^(5+3) = 2^8 = 256
a^2 times a times a^5 = a^(2+1+5) = a^8
When dividing same bases, SUBTRACT the exponents!
Examples:
x^8 / x^3 = x^(8-3) = x^5
5^6 / 5^2 = 5^(6-2) = 5^4 = 625
y^10 / y^7 = y^(10-7) = y^3
When raising a power to a power, MULTIPLY the exponents!
Examples:
(x^3)^4 = x^(3 times 4) = x^12
(2^4)^2 = 2^(4 times 2) = 2^8 = 256
(a^5)^3 = a^(5 times 3) = a^15
(for any x that is not 0)
5^0 = 1
(-3)^0 = 1
x^0 = 1
Negative = reciprocal (flip it!)
2^(-3) = 1/2^3 = 1/8
x^(-4) = 1/x^4
5^(-2) = 1/5^2 = 1/25
WRONG: x^3 times x^4 = x^12 (No! You ADD for product rule)
RIGHT: x^3 times x^4 = x^7
WRONG: x^0 = 0
RIGHT: x^0 = 1
WRONG: 2^(-3) = -8
RIGHT: 2^(-3) = 1/8
1. Simplify: x^5 times x^2 =
2. Simplify: y^9 / y^4 =
3. Simplify: (a^3)^5 =
4. Evaluate: 3^(-2) =
5. Evaluate: 7^0 =
6. Simplify: (2^3)^2 times 2^4 =