Multiply and simplify by factoring
∜10,000*∜10,000,000
I get ∜100^9
I hope this is correct
10,000 = 10^4
10,000,000 = 10^7
Is that your final answer?
So would it be 10^11 right
√ 10^11
To multiply and simplify by factoring ∜10,000 * ∜10,000,000, we can first recognize that both numbers have a common factor of 10,000. We can express both of these numbers as the fourth root of the prime factorization of 10,000.
Step 1: Prime factorize both numbers.
10,000 = 2^4 * 5^4
10,000,000 = 2^8 * 5^8
Step 2: Rewrite the expression using prime factorization.
∜10,000 * ∜10,000,000 = ∜(2^4 * 5^4) * ∜(2^8 * 5^8)
Step 3: Apply the rule of multiplying roots.
∜(2^4 * 5^4) * ∜(2^8 * 5^8) = ∜(2^4 * 2^8 * 5^4 * 5^8)
Step 4: Simplify the exponents inside the radical.
∜(2^4 * 2^8 * 5^4 * 5^8) = ∜(2^(4+8) * 5^(4+8))
Step 5: Perform the addition.
∜(2^(4+8) * 5^(4+8)) = ∜(2^12 * 5^12)
Step 6: Combine the like terms inside the radical.
∜(2^12 * 5^12) = ∜(2^12) * ∜(5^12)
Step 7: Simplify the exponents.
∜(2^12) * ∜(5^12) = 2^(12/4) * 5^(12/4)
Step 8: Simplify the expression.
2^(12/4) * 5^(12/4) = 2^3 * 5^3
Therefore, the final simplified expression is 2^3 * 5^3, or 8 * 125, which equals 1,000.