Which of the following is a like term of z^4?
Answer and explanation
Correct answer: 9z^4
The governing concept is the definition of like terms in algebra. Two terms are like terms when they contain exactly the same variables raised to exactly the same powers; their numerical coefficients may be different. The term z^4 contains the variable z with exponent 4. In 9z^4, the variable part is also z^4, and only the coefficient changes from 1 to 9, so it is a like term. Therefore, option A is correct. Although 9z^3 has the same variable, its exponent is different. z^5 also has a different exponent, and 9y^4 uses a different variable. Coefficients do not determine likeness, but the variable part and its exponent must match completely.
Frequently asked questions
What is the correct answer to this question?
9z^4
Why is this the correct answer?
The governing concept is the definition of like terms in algebra. Two terms are like terms when they contain exactly the same variables raised to exactly the same powers; their numerical coefficients may be different. The term z^4 contains the variable z with exponent 4. In 9z^4, the variable part is also z^4, and only the coefficient changes from 1 to 9, so it is a like term. Therefore, option A is correct. Although 9z^3 has the same variable, its exponent is different. z^5 also has a different exponent, and 9y^4 uses a different variable. Coefficients do not determine likeness, but the variable part and its exponent must match completely.
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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