Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Our Q&A platform provides quick and trustworthy answers to your questions from experienced professionals in different areas of expertise. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
To determine which expression is equivalent to [tex]\(\frac{(a b^2)^3}{b^5}\)[/tex], let's start by simplifying the given expression step-by-step.
1. Expand the numerator:
[tex]\[ (a b^2)^3 \][/tex]
When we raise a product to a power, every factor in the product is raised to the power separately. Therefore, we have:
[tex]\[ (a b^2)^3 = a^3 (b^2)^3 \][/tex]
2. Simplify the exponents:
We need to simplify [tex]\( (b^2)^3 \)[/tex]:
[tex]\[ (b^2)^3 = b^{2 \cdot 3} = b^6 \][/tex]
So, our numerator becomes:
[tex]\[ a^3 b^6 \][/tex]
3. Rewrite the expression with the simplified numerator:
The original expression now looks like this:
[tex]\[ \frac{a^3 b^6}{b^5} \][/tex]
4. Simplify the fraction:
To simplify the fraction [tex]\(\frac{a^3 b^6}{b^5}\)[/tex], we can subtract the exponent of [tex]\(b\)[/tex] in the denominator from the exponent of [tex]\(b\)[/tex] in the numerator:
[tex]\[ \frac{b^6}{b^5} = b^{6 - 5} = b^1 = b \][/tex]
Therefore, the expression simplifies to:
[tex]\[ a^3 \cdot b \][/tex]
So, the expression [tex]\(\frac{(a b^2)^3}{b^5}\)[/tex] simplifies to [tex]\(a^3 b\)[/tex].
Let's compare this with the given options:
A. [tex]\(a^3 b\)[/tex]
B. [tex]\(\frac{a^3}{b}\)[/tex]
C. [tex]\(\frac{a^4}{b}\)[/tex]
D. [tex]\(a^3\)[/tex]
We see that option A, [tex]\(a^3 b\)[/tex], matches our simplified expression. Therefore, the correct answer is:
A. [tex]\(a^3 b\)[/tex]
1. Expand the numerator:
[tex]\[ (a b^2)^3 \][/tex]
When we raise a product to a power, every factor in the product is raised to the power separately. Therefore, we have:
[tex]\[ (a b^2)^3 = a^3 (b^2)^3 \][/tex]
2. Simplify the exponents:
We need to simplify [tex]\( (b^2)^3 \)[/tex]:
[tex]\[ (b^2)^3 = b^{2 \cdot 3} = b^6 \][/tex]
So, our numerator becomes:
[tex]\[ a^3 b^6 \][/tex]
3. Rewrite the expression with the simplified numerator:
The original expression now looks like this:
[tex]\[ \frac{a^3 b^6}{b^5} \][/tex]
4. Simplify the fraction:
To simplify the fraction [tex]\(\frac{a^3 b^6}{b^5}\)[/tex], we can subtract the exponent of [tex]\(b\)[/tex] in the denominator from the exponent of [tex]\(b\)[/tex] in the numerator:
[tex]\[ \frac{b^6}{b^5} = b^{6 - 5} = b^1 = b \][/tex]
Therefore, the expression simplifies to:
[tex]\[ a^3 \cdot b \][/tex]
So, the expression [tex]\(\frac{(a b^2)^3}{b^5}\)[/tex] simplifies to [tex]\(a^3 b\)[/tex].
Let's compare this with the given options:
A. [tex]\(a^3 b\)[/tex]
B. [tex]\(\frac{a^3}{b}\)[/tex]
C. [tex]\(\frac{a^4}{b}\)[/tex]
D. [tex]\(a^3\)[/tex]
We see that option A, [tex]\(a^3 b\)[/tex], matches our simplified expression. Therefore, the correct answer is:
A. [tex]\(a^3 b\)[/tex]
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.