(8^4/10^4)^-1/4
(8^4/10^4)^-1/4 = ((2^3)^4/(2*5)^4)^-1/4 = (2^12/2^16)^-1/4 = (1/2^4)^-1/4 = 2
1.25
1.25 is a decimal number, it cannot be simplified any further as a fraction or exponent.
5^-1/6
5^-1/6 can be simplified using the rule of negative exponents which states that a^(-n) is equal to 1/a^n. Therefore:
5^-1/6 = 1/5^(1/6)
To solve the expression (8^4/10^4)^-1/4, we'll break it down step by step:
Step 1: Evaluate the expressions in the parentheses:
8^4 = 8 * 8 * 8 * 8 = 4096
10^4 = 10 * 10 * 10 * 10 = 10,000
So we have ((4096/10,000)^-1/4).
Step 2: Simplify the fraction inside the parentheses:
4096/10,000 = 0.4096
Now we have (0.4096^-1/4).
Step 3: Calculate the negative exponent (raise the fraction to the -1 power):
0.4096^-1 = 1/0.4096 = 2.44 (rounded to 2 decimal places)
Now our expression becomes (2.44^1/4).
Step 4: Take the fourth root of 2.44:
2.44^(1/4) ≈ 1.336 (rounded to 3 decimal places)
Therefore, the value of (8^4/10^4)^-1/4 is approximately 1.336.