Q15. - Algebra 1

Question

The probability of guessing correctly on 5 true-false questions is ${\left(\frac{1}{2}\right)}^{\mathbf{5}}$. Express this probability as a fraction without exponents.

Step-by-Step Solution

Answer

The required fraction is represented by $\frac{\mathbf{1}}{\mathbf{32}}$.

Step 1. Determine the exponent and base of provided expression as it will represent the count of its factors.

The provided expression contains $\frac{1}{2}$ as the base and 5 as its exponent.

Use the obtained base and exponent to determine the required evaluated value.

For numerator, perform multiplication of 1 by itself 5 times and for denominator, perform multiplication of 2 by itself 5 times to get the required value.

$\frac{1^5}{2^5}=\frac{1}{32}$

Step 3. Write the conclusion.

The obtained value does not contain any exponent which means that $\frac{1}{32}$ is the required fraction.