QUIZ ON INDICES

1) (ab)⁰ = 1

True

False

The expression (ab)0 is equal to 1. In any mathematical operation, any number raised to the power of 0 is always equal to 1. Therefore, the statement is true.

Explanation

The expression (ab)0 is equal to 1. In any mathematical operation, any number raised to the power of 0 is always equal to 1. Therefore, the statement is true.

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4) What is the exponent of the exponential expression 4⁵?

The exponent of the exponential expression 4^5 is 5. In this expression, 4 is the base, and 5 is the exponent, which tells you how many times to multiply the base by itself.

Explanation

The exponent of the exponential expression 4^5 is 5. In this expression, 4 is the base, and 5 is the exponent, which tells you how many times to multiply the base by itself.

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5) What is the base of the exponential expression 4³?

In the exponential expression 4^3, the number 4 is referred to as the base. The base represents the number that is repeatedly multiplied by itself a certain number of times, indicated by the exponent. In this case, the base 4 is multiplied by itself three times because the exponent is 3. So, 4^3 means 4×4×4, where 4 is multiplied by itself three times.

Explanation

In the exponential expression 4^3, the number 4 is referred to as the base. The base represents the number that is repeatedly multiplied by itself a certain number of times, indicated by the exponent. In this case, the base 4 is multiplied by itself three times because the exponent is 3. So, 4^3 means 4×4×4, where 4 is multiplied by itself three times.

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6) (a²b)³ = a⁵b³

True

False

The given statement (a2b)3 = a5b3 is not true. In order to simplify the expression (a2b)3, we need to multiply the exponents inside the parentheses by the exponent outside the parentheses. This gives us a6b3. Therefore, the correct answer is False.

Explanation

The given statement (a2b)3 = a5b3 is not true. In order to simplify the expression (a2b)3, we need to multiply the exponents inside the parentheses by the exponent outside the parentheses. This gives us a6b3. Therefore, the correct answer is False.

7) Solve: (2³)²

To solve (2^3)^2, we need to apply the power of a power rule, which states that (x^m)^n = x^(m*n)

Therefore, (2^3)^2 = 2^(3*2) = 2^6 = 64

Explanation

To solve (2^3)^2, we need to apply the power of a power rule, which states that (x^m)^n = x^(m*n)

Therefore, (2^3)^2 = 2^(3*2) = 2^6 = 64

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8) (a¹⁰b^-3)⁰ = z⁰

True

False

Explanation

9) (3)^-2

The value of (3^-2) can be found by taking the reciprocal of 3², which is (1/3²).

(3²) equals (3 x 3 = 9).

So, 3^-2 = 1/3² = 1/9

Therefore, 3^-2 equals 1/9

Explanation

The value of (3^-2) can be found by taking the reciprocal of 3², which is (1/3²).

(3²) equals (3 x 3 = 9).

So, 3^-2 = 1/3² = 1/9

Therefore, 3^-2 equals 1/9

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Quiz On Indices