(√2÷5)^8÷(√2÷5)^1/3
just use your rules of exponents
a^x ÷ a^y = a^(x-y)
you have the same base of (√2÷5)
I am not able to get the answer as 3125/4√2
Please help whether the question is wrong or correct.
To simplify the given expression (√2÷5)^8÷(√2÷5)^(1/3), we need to follow the rules of exponents:
1. Firstly, let's simplify each term inside the parentheses individually.
(√2 ÷ 5)^8 = (√2)^8 ÷ 5^8
= 2^4 ÷ 5^8 (since (√2)^2 = 2)
= 16 ÷ 390625 (since 2^4 = 16 and 5^8 = 390625)
= 1 ÷ 24414.06 (rounded to five decimal places)
(√2 ÷ 5)^(1/3) = (√2)^(1/3) ÷ 5^(1/3)
= 2^(1/6) ÷ 5^(1/3) (since (√2)^2 = 2)
= 1.12246205 ÷ 1.70997595 (using a scientific calculator or mathematical software to evaluate 2^(1/6) ≈ 1.12246205 and 5^(1/3) ≈ 1.70997595)
= 0.65696919 (rounded to eight decimal places)
2. Now we can substitute these simplified terms back into the expression:
(√2÷5)^8÷(√2÷5)^1/3
= (1 ÷ 24414.06) ÷ (0.65696919)
3. Finally, we can divide the numerator by the denominator:
1 ÷ 24414.06 ≈ 0.00004098 (rounded to eight decimal places)
0.00004098 ÷ 0.65696919 ≈ 0.00006236 (rounded to eight decimal places)
So, the simplified value of (√2÷5)^8÷(√2÷5)^(1/3) is approximately 0.00006236.