What is the simplified form of ((2^4)^2)?
Answer and explanation
Correct answer: 2^8
Use the power-of-a-power law, (a^m)^n=a^(mn). Here the inner exponent is 4 and the outer exponent is 2, so (2^4)^2=2^(4×2)=2^8. Therefore option B is the standard simplified form. Option A, 2^6, comes from adding 4 and 2, but addition is not the rule for a power raised to a power. Option C, 2^16, results from multiplying the numerical powers themselves rather than multiplying the exponents. Option D, 4^4, is numerically equivalent because 4^4=(2^2)^4=2^8, but it is not the canonical form with the original base 2. Thus the intended answer is uniquely option B under standard simplification conventions.
Frequently asked questions
What is the correct answer to this question?
2^8
Why is this the correct answer?
Use the power-of-a-power law, (a^m)^n=a^(mn). Here the inner exponent is 4 and the outer exponent is 2, so (2^4)^2=2^(4×2)=2^8. Therefore option B is the standard simplified form. Option A, 2^6, comes from adding 4 and 2, but addition is not the rule for a power raised to a power. Option C, 2^16, results from multiplying the numerical powers themselves rather than multiplying the exponents. Option D, 4^4, is numerically equivalent because 4^4=(2^2)^4=2^8, but it is not the canonical form with the original base 2. Thus the intended answer is uniquely option B under standard simplification conventions.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Operations on real numbers and the laws of exponents.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
