What is the simplified form of ((4³)²)?
Answer and explanation
Correct answer: 4⁶
The governing rule is the power-of-a-power law: (aᵐ)ⁿ=aᵐⁿ. The outer exponent multiplies the inner exponent, so (4³)²=4^(3×2)=4⁶. Therefore option B is correct. The exponents are multiplied, not added; consequently 4⁵ is not obtained from this expression. The value 4⁹ would result from another incorrect combination of the exponents. Option D, 4³, ignores the outer square and therefore also fails to preserve the value. The same result can be checked numerically: 4³=64 and 64²=4096, while 4⁶=4096. The revised fourth option is deliberately 4³ rather than an equivalent expression such as 16³, ensuring that only one listed option represents the intended simplified form.
Frequently asked questions
What is the correct answer to this question?
4⁶
Why is this the correct answer?
The governing rule is the power-of-a-power law: (aᵐ)ⁿ=aᵐⁿ. The outer exponent multiplies the inner exponent, so (4³)²=4^(3×2)=4⁶. Therefore option B is correct. The exponents are multiplied, not added; consequently 4⁵ is not obtained from this expression. The value 4⁹ would result from another incorrect combination of the exponents. Option D, 4³, ignores the outer square and therefore also fails to preserve the value. The same result can be checked numerically: 4³=64 and 64²=4096, while 4⁶=4096. The revised fourth option is deliberately 4³ rather than an equivalent expression such as 16³, ensuring that only one listed option represents the intended simplified form.
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.
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