Math Problem Statement

Solv

(1/4)^{-2} - (5^0 * 2) * 1^{-1}

Solution

The expression to evaluate is:

(14)2(502)11\left(\frac{1}{4}\right)^{-2} - \left(5^0 \cdot 2\right) \cdot 1^{-1}

Let's break this down step by step:

  1. Evaluate (14)2\left(\frac{1}{4}\right)^{-2}: (14)2=(41)2=42=16\left(\frac{1}{4}\right)^{-2} = \left(\frac{4}{1}\right)^2 = 4^2 = 16

  2. Evaluate 5025^0 \cdot 2: 50=1(since any number to the power of 0 is 1)5^0 = 1 \quad \text{(since any number to the power of 0 is 1)} 502=12=25^0 \cdot 2 = 1 \cdot 2 = 2

  3. Evaluate 111^{-1}: 11=11=11^{-1} = \frac{1}{1} = 1

  4. Multiply 2112 \cdot 1^{-1}: 21=22 \cdot 1 = 2

  5. Finally, subtract the two results: 162=1416 - 2 = 14

So, the evaluated result of the expression is:

14\boxed{14}

Would you like further details or have any questions?

Here are 5 related questions for further practice:

  1. What is the value of (13)2\left(\frac{1}{3}\right)^{-2}?
  2. Evaluate 23422^{-3} \cdot 4^2.
  3. Simplify (25)3\left(\frac{2}{5}\right)^{-3}.
  4. What is the result of 1003110^0 \cdot 3^{-1}?
  5. How would you simplify (12)44\left(\frac{1}{2}\right)^{-4} - 4?

Tip: Remember that a negative exponent means taking the reciprocal of the base and then raising it to the positive power.

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Math Problem Analysis

Mathematical Concepts

Exponents
Order of Operations

Formulas

a^{-n} = (1/a)^n
a^0 = 1

Theorems

Properties of Exponents

Suitable Grade Level

Grades 8-10