Simplify the Exponential Fraction: (15×6)^ax ÷ (15×6)^(y+1)

We are given the expression $\frac{(15 \times 6)^{ax}}{(15 \times 6)^{y+1}}$ and need to simplify it using the rules of exponents.

First, let's recall the rule: the "Power of a Quotient Rule for Exponents" which states that for any real number $a$ and any integers $m$ and $n$, $\frac{a^m}{a^n} = a^{m-n}$.

Applying this rule to our expression, we have the same base $(15 \times 6)$ in both the numerator and the denominator. Thus, we can subtract the exponent in the denominator from the exponent in the numerator.

The exponents in the numerator and the denominator are $ax$ and $y+1$ respectively. Therefore, we subtract the exponent $y+1$ from $ax$:

• Numerator's exponent: $ax$
• Denominator's exponent: $y+1$
• Exponent of the result: $ax - (y+1)$

Simplifying the exponent, we have:

$ax - (y+1) = ax - y - 1$

Therefore, the expression simplifies to:

$\left(15 \times 6\right)^{ax-y-1}$

The solution to the question is: $\left(15 \times 6\right)^{ax-y-1}$