Question

Prove that (a⁴b⁶)ᵗ= a²ᵗb⁶ᵗ for any a,b ∈ M ₘₓₙ (F) at any t
∈ F, where F is a field.

Answer 1

To prove that (a⁴b⁶)ᵗ = a²ᵗb⁶ᵗ for any a,b ∈ M ₘₓₙ (F) at any t ∈ F, where F is a field, we can use the property of exponents. First, rewrite the left side of the equation using the rule (x^a)^b = x^(a*b). Simplify further by rearranging terms using the commutative property of multiplication.

Step-by-step explanation:

To prove that (a⁴b⁶)ᵗ = a²ᵗb⁶ᵗ for any a, b ∈ Mₘₓₙ(F) at any t ∈ F, where F is a field, we can use the property of exponents.

First, let's rewrite the left side of the equation using the rule (xa)b = xa*b. So we have (a4b6)t = a4* tb6* t.

Now, we can simplify further by using the commutative property of multiplication to rearrange the terms. So, we get (a4* tb6* t) = (a4* t)(b6* t) = a2*2* tb6* t.