Simplify the Expression: b²/b¹ Using Exponent Rules

To solve the problem, we apply the quotient rule for exponents. The quotient rule states that when you divide two exponential expressions with the same base, you can subtract the exponent of the denominator from the exponent of the numerator. In mathematical terms:

$\frac{a^m}{a^n} = a^{m-n}$

Using the formula mentioned above, let's solve $\frac{b^2}{b^1}$:

• Identify the base for both the numerator and the denominator, which in this case is $b$
• Identify the exponents for the numerator and the denominator: $m = 2$ and $n = 1$
• Subtract the exponent in the denominator from the exponent in the numerator: $2 - 1 = 1$
• Rewrite the expression with the new exponent: $b^{2-1} = b^1$

Thus, $\frac{b^2}{b^1} = b^1$ as per the power of a quotient rule.

The solution to the question is: $b^1$