Simplifying radicals

What is the relationship between radicals and exponents?

• Radicals can be expressed as exponents: @@ ext{√}a = a^{rac{1}{2}}@@.

• Radicals are always greater than their corresponding exponents.

• Radicals and exponents are unrelated mathematical concepts.

• Radicals can only be expressed as whole numbers.

What is a perfect square?

• A number that can be expressed as the square of an integer

• A number that is the product of two different integers

• A number that is always even

• A number that cannot be expressed as a fraction

What does it mean to simplify a radical?

• To express it in its simplest form, removing any perfect squares or cubes from under the radical sign.

• To multiply the radical by itself to eliminate the radical sign.

• To add the radical to another radical of the same value.

• To convert the radical into a decimal approximation.

Which expression is NOT equivalent to @@6^{-2}@@?

• @@rac{1}{6^{-2}}@@ is NOT equivalent.

• @@6^2@@ is equivalent.

• @@rac{1}{36}@@ is equivalent.

• @@rac{1}{6^2}@@ is equivalent.

What is the value of any non-zero number raised to the power of 0?

• 0

• 1

• It depends on the number

• Undefined

What is a radical?

• An expression that includes a root, such as a square root (√) or cube root (∛).

• A type of polynomial that has no roots.

• A mathematical operation that involves addition and subtraction.

• A geometric figure with straight lines and angles.

How do you simplify @@ ext{√}a^2@@?

• @@a@@

• @@a^2@@

• @@ ext{√}a@@

• @@ ext{√}a^3@@

What is a negative exponent?

• A negative exponent indicates that the base should be taken as the reciprocal, for example, @@x^{-n} = rac{1}{x^n}@@.

• A negative exponent means the base is multiplied by itself a negative number of times.

• A negative exponent indicates that the base should be squared.

• A negative exponent is simply a way to express a positive number.