Calculate 2^(-5): Solving Negative Exponent Expression

Question

$2^{-5}=\text{?}$

Video Solution

Solution Steps

00:00 Solve the following problem

00:03 According to the laws of exponents, any number(A)raised to the power of(N)

00:06 is equal to 1 divided by the number(A) raised to the power of(-N)

00:10 Let's apply this to the question

00:13 The number 2 becomes a half and the power(-5) becomes -(-5)

00:18 A negative multiplied by a negative becomes a positive hence the power is 5

00:21 This is the solution

Step-by-Step Solution

We begin by using the power rule of negative exponents.

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

$2^{-5}=\frac{1}{2^5}=\frac{1}{32}$ We can therefore deduce that the correct answer is option A.

Answer

$\frac{1}{32}$

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