Evaluate the Expression: Simplifying 1/4²

Question

Insert the corresponding expression:

142= \frac{1}{4^2}=

Video Solution

Solution Steps

00:00 Simplify the following problem
00:03 According to the laws of exponents, a number raised to the power of (-N)
00:06 is equal to the reciprocal number raised to the opposite power (-N)
00:09 We will apply this formula to our exercise
00:14 We'll convert to the reciprocal number and raise it to the opposite power (times(-1))
00:17 This is the solution

Step-by-Step Solution

To solve the problem of expressing 142\frac{1}{4^2} using powers with negative exponents:

  • Identify the base in the denominator: 4 raised to the power 2.
  • Apply the rule for negative exponents that states 1an=a−n\frac{1}{a^n} = a^{-n}.
  • Express 142\frac{1}{4^2} as 4−24^{-2}.

Thus, the expression 142\frac{1}{4^2} can be rewritten as 4−2 4^{-2} .

Answer

4−2 4^{-2}

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Related Subjects

Negative Exponents Power of a Quotient Exponents - Special Cases

Question Types

Powers of a Fraction: Inverse formula Powers of a Fraction: Presenting powers in the denominator as powers with negative exponents Negative Exponents: Presenting powers in the denominator as powers with negative exponents