Questions: My IXL Learning Assessment C. 15 Identify equivalent expressions involving exponents II QDM Select all the expressions that are equivalent to 7^-6 cdot 2^-6. 14^-6 14^-12 14^36 1/14^6

My IXL Learning Assessment C. 15 Identify equivalent expressions involving exponents II QDM Select all the expressions that are equivalent to 7^-6 cdot 2^-6. 14^-6 14^-12 14^36 1/14^6
Transcript text: My IXL Learning Assessment C. 15 Identify equivalent expressions involving exponents II QDM Select all the expressions that are equivalent to $7^{-6} \cdot 2^{-6}$. $14^{-6}$ $14^{-12}$ $14^{36}$ $\frac{1}{14^{6}}$ Submit Work it out Not feeling ready yet? These can help: Identify equivalent expressions involving exponents I (100) y Lesson: Properties
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Solution

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Solution Steps

To determine which expressions are equivalent to \(7^{-6} \cdot 2^{-6}\), we can use the properties of exponents. Specifically, we can combine the bases when the exponents are the same.

Solution Approach
  1. Combine the bases of the exponents using the property \(a^{-m} \cdot b^{-m} = (a \cdot b)^{-m}\).
  2. Simplify the combined expression and compare it to the given options.
Step 1: Combine the Exponents

We start with the expression \(7^{-6} \cdot 2^{-6}\). Using the property of exponents, we can combine the bases: \[ 7^{-6} \cdot 2^{-6} = (7 \cdot 2)^{-6} = 14^{-6} \]

Step 2: Evaluate the Given Options

Next, we evaluate the provided options to see which are equivalent to \(14^{-6}\):

  • \(14^{-6}\)
  • \(14^{-12}\)
  • \(14^{36}\)
  • \(\frac{1}{14^{6}}\)
Step 3: Compare with the Simplified Expression

From our calculations, we find that:

  • \(14^{-6} = 1.3281 \times 10^{-07}\)
  • \(\frac{1}{14^{6}} = 1.3281 \times 10^{-07}\)
  • \(14^{-12} = 1.7639 \times 10^{-14}\)
  • \(14^{36} = 182225556172186058674940229804729969934336\)

The expressions \(14^{-6}\) and \(\frac{1}{14^{6}}\) are equivalent to \(7^{-6} \cdot 2^{-6}\).

Final Answer

The equivalent expressions are \(14^{-6}\) and \(\frac{1}{14^{6}}\). Thus, the answer is: \[ \boxed{14^{-6}, \frac{1}{14^{6}}} \]

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