Algebra 2 Unit 8.2 Apply Properties of Rational Exponents

STUDY
PLAY
9÷9∧⁻4/5
9∧9/5
x∧1/4 × x1/3
X ∧7/12
2/x∧-1/4
2x∧1/4
(x∧15)/y∧6
x∧5/y∧2
7 3square root 125
125= 5×25=5×5 = 5×7 =35
Simplify 5∧3/2 × 5∧1/2
5∧4/2 = 5²
= 25
Simplify 2/X∧⁻¼
2x∧¼
Simplify (2∧1/3 × 5∧1/6)⁶
2² × 5¹ = 4 × 5
= 20
Simplify (X¹⁵/Y⁶)∧1/3
X⁵/Y²
Simplify −³√10 × −4³√100
4³√10 ×100 = 4³√10 × 10 × 10
4 × 10 = 40
use the product to a power rule to solve
(ab)²
a²b²
simplify 11∧¼÷11∧¾
11∧½
combine these radicals
2²√3 + 2²√3
4²√3
use the quotient rule to solve
a∧m÷ aⁿ
a∧m−n
what is the multiplication rule?
a∧m+a∧n = a∧mn
Simplify
5∧3/2 × 5∧1/2
5∧4/2 = 5∧2
=25
Simplify
2x∧1/2 × 4x^3/4
=8x^5/4
Simplify
x^1/4 × x^1/3
=x^7/12
Simplify
(64y^8)^1/2
64^1/2y^4
=8y^4
Simplify
5x^2/3 + (x^5/4)^8/15
5x^2/3 + x^2/3
=6x^2/3
-3(^4√4) -2(^4√64)
-7(^4√4)
(3^3/7^3)^-1\3
7\3
^3√-216n^4
6n(^3√n)
-7^3√108x^7 y^5
-21x^4 y^2 ^3√4
9\9^-4/5
9^9\5
simplify 5^3/2 x 5^1/2
5^4/2= 5²
=25
simplify 7 ³√125
7³√25x5
7 ³√5x5x5
7x5
=35
simplify 2/x^-1/4
2x¼
simplify (64y^8)½
6y½ y^4
=8y^4
simplify 2x½ x 4x¾
8x^5/4
adv exp.
simplest form of radicals:
no perfect nth powers as factors and any denominator has been rationalized.
a^m * a^n =
a∧m+n
a^-m =
1 / a^m
ax^m ± bx^m =
(a + b)x^m
a^m / a^n
a^m-n