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What is the simplified form of ((4^3)^2)?

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Answer and explanation

Correct answer: 4^6

The governing exponent law is the power-of-a-power rule: (a^m)^n = a^(mn). The outer exponent 2 multiplies the inner exponent 3, so (4^3)^2 = 4^(3×2) = 4^6. Therefore option B is correct. Notice that 4^5 would result from incorrectly adding exponents, which is not valid for a power raised to another power. The expression 4^9 is also produced by an incorrect combination of the exponents. Option D, 16^3, is actually numerically equivalent because 16^3 = (4^2)^3 = 4^6, but it is not the intended simplified form using the given base and is therefore not the best unique answer. The standard simplified form is 4^6.

Related tags

ExponentsPower-Of-A-PowerMathematicsOperations On Real Numbers And The Laws Of ExponentsPolynomialsClass 10 Mcq

Frequently asked questions

What is the correct answer to this question?

4^6

Why is this the correct answer?

The governing exponent law is the power-of-a-power rule: (a^m)^n = a^(mn). The outer exponent 2 multiplies the inner exponent 3, so (4^3)^2 = 4^(3×2) = 4^6. Therefore option B is correct. Notice that 4^5 would result from incorrectly adding exponents, which is not valid for a power raised to another power. The expression 4^9 is also produced by an incorrect combination of the exponents. Option D, 16^3, is actually numerically equivalent because 16^3 = (4^2)^3 = 4^6, but it is not the intended simplified form using the given base and is therefore not the best unique answer. The standard simplified form is 4^6.

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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