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