Simplify the Expression: 1/(2×3)^(-5) Using Negative Exponents

Insert the corresponding expression:

$\frac{1}{\left(2\times3\right)^{-5}}=$

To solve this problem, we'll follow these steps:

• Step 1: Identify the given expression: $\frac{1}{(2 \times 3)^{-5}}$.
• Step 2: Apply the negative exponent rule. This rule states that $\frac{1}{a^{-n}} = a^{n}$.
• Step 3: Simplify the expression.

Now, let's work through each step:

Step 1: The problem gives us the expression $\frac{1}{(2 \times 3)^{-5}}$.

Step 2: Apply the negative exponent rule:

Given $\frac{1}{(2 \times 3)^{-5}}$, we use the formula for negative exponents, which means:

$(a \times b)^{-n} = \frac{1}{(a \times b)^{n}}$

We can rewrite $\frac{1}{(2 \times 3)^{-5}}$ as $(2 \times 3)^{5}$.

There is no need for further simplification, as the problem asks only for the equivalent expression.

Therefore, the expression $\frac{1}{(2 \times 3)^{-5}}$ simplifies to $(2 \times 3)^{5}$.

The correct answer is $(2 \times 3)^{5}$.