Calculate the Fraction: Finding the Value of 1/2^9

Question

$\frac{1}{2^9}=\text{?}$

Video Solution

Solution Steps

00:00 Solve the following problem

00:02 According to the laws of exponents, a number(A) when raised to the power of(-N)

00:05 equals 1 divided by the number(A) raised to the power of(N)

00:08 Let's apply this to the question, the formula works from the number to the fraction and vice versa

00:11 The number 1 divided by (2) becomes 2

00:14 and the exponent (9) becomes (-9)

00:16 This is the solution

Step-by-Step Solution

We use the power property for a negative exponent:

$a^{-n}=\frac{1}{a^n}$ We apply it to the given expression:

$\frac{1}{2^9}=2^{-9}$

Therefore, the correct answer is option A.

Answer

$2^{-9}$

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Negative Exponents Exponents and Exponent rules Rules of Exponentiation Combining Powers and Roots Properties of Exponents Exponents - Special Cases

Question Types

Applying Combined Exponents Rules: Calculating powers with negative exponents Applying Combined Exponents Rules: Presenting powers in the denominator as powers with negative exponents Applying Combined Exponents Rules: Presenting powers with negative exponents as fractions Applying Combined Exponents Rules: Monomial Negative Exponents: Calculating powers with negative exponents Negative Exponents: Presenting powers in the denominator as powers with negative exponents Negative Exponents: Presenting powers with negative exponents as fractions