Question

(x^4)^3=(x^3)^4 true or false

13^4 x 13^7= (13^4)^7 true or false
y^5xy^0/y^3=(y^2)^1 true or false
q^0xq^5/q^2=(q^3)^2/q^3

Answer 1

`1) { ({x}^(4))}^(3) = { ({x}^(3) )}^(4) \\ power \: multiply \\ {x}^(12) = {x}^(12) = > true \\ 2) {13}^(4) * {13}^(7) = \\ power \: add \\ {13}^(11) not \: = { {13}^(4) }^(7) \\ = > false \\ 3) \frac{ {y}^(5) {y}^(0) }{ {y}^(3) } = { {y}^(2) }^(1) \\ {y}^(2) = {y}^(2) \\ = > true \\ 4) \frac{ {q}^(0){q}^(5) }{ {q}^(2) } = \frac{ { {q}^(3) }^(2) }{ {q}^(3) } \\ {q}^(3) = {q}^(3) \\ = > true \\ thank \: you`

Answer 2

Explanation:

(x^4)^3=(x^3)^4 , true

=> x^(4×3) = x^(3×4) = x^12

13^4 x 13^7= (13^4)^7, false

13^(4+7) = 13^11

(13^4)^7 = 13^(4×7) = 13^28

y^5 x y^0/y^3=(y^2)^1 , true

y^5 x y^0/y^3 = y^(5+0-3) = y^2

(y^2)^1 = y^(2×1) = y^2

q^0 x q^5/q^2=(q^3)^2/q^3, true

q^0 x q^5/q^2= q^(0+5-2)= q^3

(q^3)^2/q^3 = q^(3×2-3) = q^3