Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Get detailed and accurate answers to your questions from a community of experts on our comprehensive Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
To simplify [tex]\(\left(2^{-5} \times 2^8\right)^2\)[/tex], we will utilize the properties of exponents step by step:
### Step 1: Simplify the expression inside the parentheses
We start by simplifying the expression [tex]\(2^{-5} \times 2^8\)[/tex] which is inside the parentheses.
Using the property of exponents that states [tex]\(a^m \times a^n = a^{m+n}\)[/tex]:
[tex]\[ 2^{-5} \times 2^8 = 2^{-5 + 8} \][/tex]
### Step 2: Combine the exponents
Next, we perform the addition in the exponent:
[tex]\[ -5 + 8 = 3 \][/tex]
So, the expression simplifies to:
[tex]\[ 2^3 \][/tex]
Now, our original problem [tex]\(\left(2^{-5} \times 2^8\right)^2\)[/tex] has been simplified to [tex]\((2^3)^2\)[/tex].
### Step 3: Raise the simplified expression to the power of 2
The next step is to raise [tex]\(2^3\)[/tex] to the power of 2.
Using the property of exponents [tex]\((a^m)^n = a^{m \times n}\)[/tex]:
[tex]\[ (2^3)^2 = 2^{3 \times 2} \][/tex]
### Step 4: Multiply the exponents
Perform the multiplication in the exponent:
[tex]\[ 3 \times 2 = 6 \][/tex]
Thus, [tex]\((2^3)^2\)[/tex] simplifies to:
[tex]\[ 2^6 \][/tex]
So, the simplified form of [tex]\(\left(2^{-5} \times 2^8\right)^2\)[/tex] is [tex]\(\boxed{2^6}\)[/tex].
### Step 1: Simplify the expression inside the parentheses
We start by simplifying the expression [tex]\(2^{-5} \times 2^8\)[/tex] which is inside the parentheses.
Using the property of exponents that states [tex]\(a^m \times a^n = a^{m+n}\)[/tex]:
[tex]\[ 2^{-5} \times 2^8 = 2^{-5 + 8} \][/tex]
### Step 2: Combine the exponents
Next, we perform the addition in the exponent:
[tex]\[ -5 + 8 = 3 \][/tex]
So, the expression simplifies to:
[tex]\[ 2^3 \][/tex]
Now, our original problem [tex]\(\left(2^{-5} \times 2^8\right)^2\)[/tex] has been simplified to [tex]\((2^3)^2\)[/tex].
### Step 3: Raise the simplified expression to the power of 2
The next step is to raise [tex]\(2^3\)[/tex] to the power of 2.
Using the property of exponents [tex]\((a^m)^n = a^{m \times n}\)[/tex]:
[tex]\[ (2^3)^2 = 2^{3 \times 2} \][/tex]
### Step 4: Multiply the exponents
Perform the multiplication in the exponent:
[tex]\[ 3 \times 2 = 6 \][/tex]
Thus, [tex]\((2^3)^2\)[/tex] simplifies to:
[tex]\[ 2^6 \][/tex]
So, the simplified form of [tex]\(\left(2^{-5} \times 2^8\right)^2\)[/tex] is [tex]\(\boxed{2^6}\)[/tex].
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.