Math Problem Statement

Tentukan nilai dari 2^{-6}!

Solution

The problem in the image asks:

"Tentukan nilai dari 262^{-6}!", which translates to "Determine the value of 262^{-6}"!

To solve 262^{-6}:

The negative exponent rule tells us that: ab=1aba^{-b} = \frac{1}{a^b} So, 26=1262^{-6} = \frac{1}{2^6}.

Now, calculate 262^6: 26=2×2×2×2×2×2=642^6 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 64

Thus: 26=1642^{-6} = \frac{1}{64}

The value of 262^{-6} is 164\frac{1}{64}.

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Here are 5 related questions you might find interesting:

  1. What is the value of 282^{-8}?
  2. How do you simplify expressions with negative exponents?
  3. What is the result of 343^{-4}?
  4. How can you express 262^{-6} as a decimal?
  5. What is the general formula for calculating negative exponents?

Tip: When dealing with negative exponents, remember that the negative sign in the exponent means you are taking the reciprocal of the base raised to the positive exponent!

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Math Problem Analysis

Mathematical Concepts

Exponents
Negative Exponents

Formulas

a^{-b} = 1/a^b

Theorems

Negative Exponent Rule

Suitable Grade Level

Grades 7-9