Answer :
To simplify the expression [tex]\((3y^7)^4\)[/tex], we need to apply the power of a power property in exponents, which states that [tex]\((a^m)^n = a^{m \cdot n}\)[/tex]. Let's break it down step by step:
1. Understand the Expression:
- We have [tex]\((3y^7)^4\)[/tex].
- The expression [tex]\((3y^7)^4\)[/tex] means both the coefficient (3) and the base of the variable term ([tex]\(y^7\)[/tex]) are raised to the power of 4.
2. Apply the Power to the Coefficient:
- The coefficient inside the parentheses is 3.
- Calculate [tex]\(3^4\)[/tex]. This means multiplying 3 by itself 4 times:
[tex]\[3 \times 3 \times 3 \times 3 = 81\][/tex]
3. Apply the Power to the Variable Term:
- The base inside the parentheses is [tex]\(y^7\)[/tex].
- Use the power of a power property: [tex]\((y^7)^4\)[/tex].
- This becomes [tex]\(y^{7 \cdot 4}\)[/tex] because when raising a power to another power, you multiply the exponents.
- Calculate [tex]\(7 \times 4 = 28\)[/tex].
4. Combine the Results:
- The simplified expression is [tex]\(81y^{28}\)[/tex].
Thus, [tex]\(\left(3y^7\right)^4\)[/tex] simplifies to [tex]\(81y^{28}\)[/tex].
The correct answer is [tex]\(81y^{28}\)[/tex].
1. Understand the Expression:
- We have [tex]\((3y^7)^4\)[/tex].
- The expression [tex]\((3y^7)^4\)[/tex] means both the coefficient (3) and the base of the variable term ([tex]\(y^7\)[/tex]) are raised to the power of 4.
2. Apply the Power to the Coefficient:
- The coefficient inside the parentheses is 3.
- Calculate [tex]\(3^4\)[/tex]. This means multiplying 3 by itself 4 times:
[tex]\[3 \times 3 \times 3 \times 3 = 81\][/tex]
3. Apply the Power to the Variable Term:
- The base inside the parentheses is [tex]\(y^7\)[/tex].
- Use the power of a power property: [tex]\((y^7)^4\)[/tex].
- This becomes [tex]\(y^{7 \cdot 4}\)[/tex] because when raising a power to another power, you multiply the exponents.
- Calculate [tex]\(7 \times 4 = 28\)[/tex].
4. Combine the Results:
- The simplified expression is [tex]\(81y^{28}\)[/tex].
Thus, [tex]\(\left(3y^7\right)^4\)[/tex] simplifies to [tex]\(81y^{28}\)[/tex].
The correct answer is [tex]\(81y^{28}\)[/tex].
