Rules
What do you do when two powers with the same base are being multiplied?
Name ALL of the rules needed to simplify this expression.
(xy5)8
Power Rule
Simplify:
(xy5)8
x^8y^40
Simplify:
(15x^2y^5z^6)(x^11y^9z^3)
15x^13y^14z^9
Simplify:
(x^-5y^12)^0 (x^-4y^-8)^0
1
What happens when you have 0 as the exponent?
Zero Exponent Rule: It simplifies to 1.
Name ALL of the rules needed to simplify this exponent.
(12d^6q^5r^4)/(24d^2q^4r^2)
Quotient Rule
Simplify:
(12d^6q^5r^4)/(24d^2q^4r^2)
(d^4q r^2) /2
Simplify:
(x^2y^4z^-3x^3)/y^2
(x^5y^2)/z^3
Simplify:
(2x^2y^-3)^-3
(y^9)/(8x^6)
What do you do with the exponents when applying the Power Rule?
Multiply the exponents because there is an exponent outside parentheses.
Name ALL of the rules needed to simplify this exponent.
(x^3y^2*x^8y)/(x^2y^3)
Product Rule and Quotient Rule
Simplify:
(x^3y^2*x^8y)/(x^2y^3)
x^9
Simplify:
((10x^11)(9x^-3)) /(3x^4)
30x4
Simplify:
(x^3(y^4z^6)^-2 )/(xy^2)
x^2 / (y^10z^12)
What do you do with the exponents when dividing powers with the same base?
Quotient Rule: Subtract the exponents
Name ALL of the rules needed to simplify this exponent.
((2x^2y^6z)^3)/(xy^4z^2)
Power Rule and Quotient Rule
Simplify:
((2x^2y^6z)^3)/(xy^4z^2)
8x^5y^14z
Simplify:
(x3y-5)-3 x2y0
(y^15)/x^7
Simplify:
(b^4y^0x^-2) / (a^2b^-2)
(b^6) / (a^2x^2)
When you have a negative exponent, what do you do to make it positive?
If the base with the negative exponent is in denominator, the power gets moved to the numerator.
If the base with the negative exponent is in the numerator, the power gets moved to the denominator.
Name ALL of the rules needed to simplify this exponent.
((x^3 y^8)^4 x^3y) / (x^2y^3)
Power Rule, Product Rule & Quotient Rule
Simplify:
((x^3 y^8)^4 x^3y) / (x^2y^3)
x^13y^30
Simplify:
(x^3(y^4z^6)^-2) /(4y^2)
x^3 /(4y^10z^12)
Simplify:
(2(a^4b^3c^2)^-2) /(6a^3bc^4)
1/(3a^11b^7c^8)