Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
Let's simplify the given expression step-by-step:
Given expression:
[tex]\[ \frac{6ab}{\left(a^0 b^2\right)^4} \][/tex]
Step 1: Simplify the denominator.
[tex]\[ \left(a^0 b^2\right)^4 \][/tex]
We use the properties of exponents here. Recall that any number raised to the power of 0 is 1, so [tex]\(a^0 = 1\)[/tex]. Hence,
[tex]\[ \left(a^0 b^2\right)^4 = \left(1 \cdot b^2\right)^4 = (b^2)^4 \][/tex]
Using the power of a power rule, [tex]\((b^2)^4 = b^{2 \cdot 4} = b^8\)[/tex].
Hence, our denominator simplifies to:
[tex]\[ b^8 \][/tex]
Step 2: Simplify the fraction.
We now have:
[tex]\[ \frac{6ab}{b^8} \][/tex]
We can simplify this by subtracting the exponents of [tex]\(b\)[/tex] in the numerator and the denominator. Since there is a [tex]\(b\)[/tex] (which is [tex]\(b^1\)[/tex]) in the numerator, we have:
[tex]\[ b^8 = b^{8-1} = b^7 \][/tex]
So our expression becomes:
[tex]\[ \frac{6a}{b^7} \][/tex]
Thus, the expression equivalent to the given one is:
[tex]\[ \frac{6a}{b^7} \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{A} \][/tex]
Given expression:
[tex]\[ \frac{6ab}{\left(a^0 b^2\right)^4} \][/tex]
Step 1: Simplify the denominator.
[tex]\[ \left(a^0 b^2\right)^4 \][/tex]
We use the properties of exponents here. Recall that any number raised to the power of 0 is 1, so [tex]\(a^0 = 1\)[/tex]. Hence,
[tex]\[ \left(a^0 b^2\right)^4 = \left(1 \cdot b^2\right)^4 = (b^2)^4 \][/tex]
Using the power of a power rule, [tex]\((b^2)^4 = b^{2 \cdot 4} = b^8\)[/tex].
Hence, our denominator simplifies to:
[tex]\[ b^8 \][/tex]
Step 2: Simplify the fraction.
We now have:
[tex]\[ \frac{6ab}{b^8} \][/tex]
We can simplify this by subtracting the exponents of [tex]\(b\)[/tex] in the numerator and the denominator. Since there is a [tex]\(b\)[/tex] (which is [tex]\(b^1\)[/tex]) in the numerator, we have:
[tex]\[ b^8 = b^{8-1} = b^7 \][/tex]
So our expression becomes:
[tex]\[ \frac{6a}{b^7} \][/tex]
Thus, the expression equivalent to the given one is:
[tex]\[ \frac{6a}{b^7} \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{A} \][/tex]
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated 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 trusted source for answers. Visit us again to find more information on diverse topics.