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

Video Solution

Solution Steps

00:00 Simplify the following problem

00:03 Apply the exponent laws in order to simplify the negative exponents

00:06 Convert to the reciprocal number and raise it to the power of (-1)

00:10 We'll apply this formula to our exercise

00:13 Convert to the reciprocal number (1 divided by the number)

00:17 Raise to the power of (-1)

00:20 This is the solution

Step-by-Step Solution

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 $(2 \times 3)^{5}$ .