Question

u5d1: rational exponents
score: 9/28 answered: 12/28
question 1
evaluate each expression (using exponent rules). no calculator.
$6^{\frac{1}{2}} \bullet 6^{\frac{1}{2}}$

Explanation:

Step1: Apply exponent product rule

When multiplying exponents with the same base, we add the exponents: \(a^m \cdot a^n = a^{m + n}\). Here, \(a = 6\), \(m=\frac{1}{2}\), \(n=\frac{1}{2}\). So \(6^{\frac{1}{2}} \cdot 6^{\frac{1}{2}} = 6^{\frac{1}{2}+\frac{1}{2}}\)

Step2: Simplify the exponent

\(\frac{1}{2}+\frac{1}{2} = 1\), so the expression becomes \(6^1\)

Step3: Evaluate \(6^1\)

Any number to the power of 1 is itself, so \(6^1 = 6\)

Answer:

6