Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Join our platform to connect with experts ready to provide detailed answers to your questions in various areas. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
To simplify the given expression [tex]\(\left(\frac{1}{2}\right)^{-3} \times\left(\frac{1}{4}\right)^{-3} \times\left(\frac{1}{5}\right)^{-3}\)[/tex], let's follow these steps:
### Step 1: Apply the Negative Exponent Rule
The negative exponent rule states that [tex]\( a^{-n} = \frac{1}{a^n} \)[/tex]. Therefore, we can rewrite each term in the product as follows:
[tex]\[ \left(\frac{1}{2}\right)^{-3} = 2^3 \][/tex]
[tex]\[ \left(\frac{1}{4}\right)^{-3} = 4^3 \][/tex]
[tex]\[ \left(\frac{1}{5}\right)^{-3} = 5^3 \][/tex]
### Step 2: Simplify Each Term
Now, calculate the powers:
[tex]\[ 2^3 = 2 \times 2 \times 2 = 8 \][/tex]
[tex]\[ 4^3 = 4 \times 4 \times 4 = 64 \][/tex]
[tex]\[ 5^3 = 5 \times 5 \times 5 = 125 \][/tex]
### Step 3: Calculate the Product of the Simplified Terms
Finally, multiply the results obtained in step 2:
[tex]\[ 8 \times 64 \times 125 \][/tex]
Given that:
[tex]\[ 8 \times 64 = 512 \][/tex]
And,
[tex]\[ 512 \times 125 = 64000 \][/tex]
Thus, the simplified form of the given expression [tex]\(\left(\frac{1}{2}\right)^{-3} \times\left(\frac{1}{4}\right)^{-3} \times\left(\frac{1}{5}\right)^{-3}\)[/tex] is:
[tex]\[ 64000 \][/tex]
So the final answer is:
[tex]\[ \left(\frac{1}{2}\right)^{-3} \times\left(\frac{1}{4}\right)^{-3} \times\left(\frac{1}{5}\right)^{-3} = 64000 \][/tex]
### Step 1: Apply the Negative Exponent Rule
The negative exponent rule states that [tex]\( a^{-n} = \frac{1}{a^n} \)[/tex]. Therefore, we can rewrite each term in the product as follows:
[tex]\[ \left(\frac{1}{2}\right)^{-3} = 2^3 \][/tex]
[tex]\[ \left(\frac{1}{4}\right)^{-3} = 4^3 \][/tex]
[tex]\[ \left(\frac{1}{5}\right)^{-3} = 5^3 \][/tex]
### Step 2: Simplify Each Term
Now, calculate the powers:
[tex]\[ 2^3 = 2 \times 2 \times 2 = 8 \][/tex]
[tex]\[ 4^3 = 4 \times 4 \times 4 = 64 \][/tex]
[tex]\[ 5^3 = 5 \times 5 \times 5 = 125 \][/tex]
### Step 3: Calculate the Product of the Simplified Terms
Finally, multiply the results obtained in step 2:
[tex]\[ 8 \times 64 \times 125 \][/tex]
Given that:
[tex]\[ 8 \times 64 = 512 \][/tex]
And,
[tex]\[ 512 \times 125 = 64000 \][/tex]
Thus, the simplified form of the given expression [tex]\(\left(\frac{1}{2}\right)^{-3} \times\left(\frac{1}{4}\right)^{-3} \times\left(\frac{1}{5}\right)^{-3}\)[/tex] is:
[tex]\[ 64000 \][/tex]
So the final answer is:
[tex]\[ \left(\frac{1}{2}\right)^{-3} \times\left(\frac{1}{4}\right)^{-3} \times\left(\frac{1}{5}\right)^{-3} = 64000 \][/tex]
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.