Exponents and Roots MCQs with Answers & Explanations

By the rules of negative exponents, moving the base to the denominator makes the exponent positive. Thus, a^-5 is rewritten as 1/a^5.

The expression 10^-3 translates to 1/(10^3). Since 10^3 equals 1000, the final simplified value is 1/1000 (or 0.001).

A negative exponent on a fraction flips the fraction (takes the reciprocal) and makes the exponent positive. So, (1/2)^-2 becomes (2/1)^2, which equals 4.

Raising a fraction to the power of -1 simply means finding its reciprocal. Flipping the numerator and denominator of 2/3 gives the result 3/2.

First, add the exponents: 3 + (-5) = -2, giving x^-2. Then, convert the negative exponent to a positive one by rewriting it as 1/x^2.

A fractional exponent of 1/2 is equivalent to taking the square root. The square root of 9 is 3, because 3 * 3 = 9.

An exponent of 1/4 indicates the fourth root of the base. The fourth root of 16 is 2, since 2 * 2 * 2 * 2 equals 16.

Raising a number to the power of 1/3 is the same as finding its cube root. The cube root of 8 is 2, because 2^3 = 8.

An exponent of 1/3 means calculating the cube root. Since 3 * 3 * 3 = 27, the cube root of 27 is 3.

The power of 1/2 corresponds to the square root of the number. The square root of 25 is 5, as 5 multiplied by itself equals 25.

An exponent of 1/5 asks for the fifth root of the number. The fifth root of 32 is 2, because multiplying 2 by itself five times yields 32.

The fractional power 1/3 translates to the cube root. The cube root of 64 is 4, since 4^3 (or 4 * 4 * 4) equals 64.

Raising to the 1/4 power means taking the fourth root. The number that multiplies by itself 4 times to equal 81 is 3 (3 * 3 * 3 * 3 = 81).

The exponent 1/2 is equivalent to the principal square root. The square root of 100 is 10, because 10 * 10 = 100.

Raising to the power of 1/3 means finding the cube root. The cube root of 125 is 5, since 5 cubed (5 * 5 * 5) is equal to 125.

The square root function finds a number that, when squared, equals the value inside. Because 6 * 6 = 36, the square root of 36 is 6.

Evaluating the square root of a perfect square like 49 requires finding the number that multiplies by itself to get 49, which is exactly 7.

The principal square root of 64 is the positive number that yields 64 when squared. Since 8^2 is 64, sqrt(64) equals 8.

Since 144 is a perfect square, its square root is an integer. 12 multiplied by 12 gives 144, making 12 the correct answer.

Finding the square root of 121 means identifying what positive number squared gives 121. The answer is 11, because 11 * 11 = 121.