Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
Certainly! Let's simplify the given expression step by step.
Given expression:
[tex]\[ h^9 k^{-4} \times 4 h^6 k^{-5} \div \left(10 h^2 k^{-3}\right)^{-2} \][/tex]
### Step 1: Simplify the denominator [tex]\((10 h^2 k^{-3})^{-2}\)[/tex]
When we apply the exponent [tex]\(-2\)[/tex] to the entire term inside the parentheses, we need to distribute [tex]\(-2\)[/tex] to each factor inside.
[tex]\[ (10 h^2 k^{-3})^{-2} = 10^{-2} h^{2 \cdot -2} k^{-3 \cdot -2} \][/tex]
This simplifies to:
[tex]\[ 10^{-2} h^{-4} k^6 \][/tex]
### Step 2: Rewrite the original expression using this simplified denominator
The original expression now looks like:
[tex]\[ h^9 k^{-4} \times 4 h^6 k^{-5} \times 10^{-2} h^{-4} k^6 \][/tex]
### Step 3: Combine the like terms
We need to combine the coefficients and the exponents of like bases (i.e., [tex]\(h\)[/tex] terms and [tex]\(k\)[/tex] terms).
### Coefficients:
The coefficients are [tex]\(1\)[/tex] (from [tex]\(h^9 k^{-4}\)[/tex]), [tex]\(4\)[/tex] (from [tex]\(4 h^6 k^{-5}\)[/tex]), and [tex]\(10^{-2}\)[/tex]:
[tex]\[ 1 \times 4 \times 10^{-2} = 4 \times \frac{1}{100} = \frac{4}{100} = \frac{1}{25} \][/tex]
### Exponents of [tex]\(h\)[/tex]:
Combine the exponents of [tex]\(h\)[/tex]:
[tex]\[ h^{9 + 6 - 4} = h^{11} \][/tex]
### Exponents of [tex]\(k\)[/tex]:
Combine the exponents of [tex]\(k\)[/tex]:
[tex]\[ k^{-4 - 5 + 6} = k^{-3} \][/tex]
### Step 4: Construct the final simplified expression
Putting it all together, we have:
[tex]\[ \frac{1}{25} \times h^{11} \times k^{-3} = \frac{h^{11}}{25 k^3} \][/tex]
Thus, the fully simplified expression is:
[tex]\[ \boxed{\frac{h^{11}}{25 k^3}} \][/tex]
Given expression:
[tex]\[ h^9 k^{-4} \times 4 h^6 k^{-5} \div \left(10 h^2 k^{-3}\right)^{-2} \][/tex]
### Step 1: Simplify the denominator [tex]\((10 h^2 k^{-3})^{-2}\)[/tex]
When we apply the exponent [tex]\(-2\)[/tex] to the entire term inside the parentheses, we need to distribute [tex]\(-2\)[/tex] to each factor inside.
[tex]\[ (10 h^2 k^{-3})^{-2} = 10^{-2} h^{2 \cdot -2} k^{-3 \cdot -2} \][/tex]
This simplifies to:
[tex]\[ 10^{-2} h^{-4} k^6 \][/tex]
### Step 2: Rewrite the original expression using this simplified denominator
The original expression now looks like:
[tex]\[ h^9 k^{-4} \times 4 h^6 k^{-5} \times 10^{-2} h^{-4} k^6 \][/tex]
### Step 3: Combine the like terms
We need to combine the coefficients and the exponents of like bases (i.e., [tex]\(h\)[/tex] terms and [tex]\(k\)[/tex] terms).
### Coefficients:
The coefficients are [tex]\(1\)[/tex] (from [tex]\(h^9 k^{-4}\)[/tex]), [tex]\(4\)[/tex] (from [tex]\(4 h^6 k^{-5}\)[/tex]), and [tex]\(10^{-2}\)[/tex]:
[tex]\[ 1 \times 4 \times 10^{-2} = 4 \times \frac{1}{100} = \frac{4}{100} = \frac{1}{25} \][/tex]
### Exponents of [tex]\(h\)[/tex]:
Combine the exponents of [tex]\(h\)[/tex]:
[tex]\[ h^{9 + 6 - 4} = h^{11} \][/tex]
### Exponents of [tex]\(k\)[/tex]:
Combine the exponents of [tex]\(k\)[/tex]:
[tex]\[ k^{-4 - 5 + 6} = k^{-3} \][/tex]
### Step 4: Construct the final simplified expression
Putting it all together, we have:
[tex]\[ \frac{1}{25} \times h^{11} \times k^{-3} = \frac{h^{11}}{25 k^3} \][/tex]
Thus, the fully simplified expression is:
[tex]\[ \boxed{\frac{h^{11}}{25 k^3}} \][/tex]
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.