Can some one help me with these two problems
multiply and simplify by factoring
∜10000*∜100000
type exact answer, using radicals as needed
2) Rewrite with rational exponents
(�ã3mn)^3
the (mn) are included under the square root as well.
Certainly! I'll help you with the two problems step by step:
1) Multiply and simplify by factoring: ∜10000 * ∜100000
To simplify this expression, we'll start by factoring the numbers under the fourth roots:
∜10000 = ∜(2^4 * 5^4)
∜100000 = ∜(10^4 * 10^1)
Next, we'll use the property of radicals that states ∜(a * b) = ∜a * ∜b:
∜(2^4 * 5^4) * ∜(10^4 * 10^1)
= (∜2^4 * ∜5^4) * (∜10^4 * ∜10^1)
Now, let's simplify each of the radicals:
∜2^4 = 2
∜5^4 = 5
∜10^4 = 10
∜10^1 = √10
Substituting these values back into the expression:
2 * 5 * 10 * √10
To write the answer using radicals as needed, we can simplify further:
2 * 5 = 10
10 * 10 = 100
So, the final answer is 100√10.
2) Rewrite with rational exponents: (�ã3mn)^3
In order to rewrite the expression with rational exponents, we'll use the property that states (√a)^n = a^(n/2).
Applying this property to our expression:
(�ã3mn)^3 = (3mn)^(3/2)
So, the expression rewritten with rational exponents is (3mn)^(3/2).