8^2/3+4^3/2÷16^-3/4
To solve this problem, we can start by simplifying the exponents.
8^2/3 = (2^3)^2/3 = 2^6/3 = 64^(1/3) = 4
4^3/2 = 2^6/2 = 2^3 = 8
16^-3/4 = (2^4)^-3/4 = 2^-12/4 = 2^-3 = 1/8
Now we can substitute these values back into the expression:
8^2/3 + 4^3/2 ÷ 16^-3/4 = 4 + 8 ÷ (1/8)
Next, we will simplify the division:
8 ÷ (1/8) = 8 * 8 = 64
Finally, we can substitute this value back into the expression:
4 + 64 = 68
Therefore, 8^2/3 + 4^3/2 ÷ 16^-3/4 equals 68.
To solve this expression step-by-step, we need to follow the rules of operations, which is often abbreviated as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Let's break down the expression:
1. Start by evaluating the exponents:
- 8^2 = 64
- 4^3 = 64
- 16^-3/4 = 1/16^(3/4) ≈ 1/2 (since 16^1/4 = √16 = 4)
2. Next, perform the division:
- 8^2/3 = 64/3
- 4^3/2 = 64/2
3. Simplify further:
- 64/3 ≈ 21.33
- 64/2 = 32
4. Finally, perform the addition of the two results:
- 21.33 + 32 ≈ 53.33
Therefore, 8^2/3 + 4^3/2 ÷ 16^-3/4 is approximately equal to 53.33.