Radicals & Rational Exponents

Front

What is a radical in mathematics?

Back

A radical is a symbol that represents the root of a number, typically the square root, cube root, etc.

Front

What is a rational exponent?

Back

A rational exponent is an exponent that is a fraction, where the numerator indicates the power and the denominator indicates the root.

Front

How do you convert a radical expression to exponential form?

Back

To convert a radical expression to exponential form, express the root as a fractional exponent. For example, ∛x can be written as x^(1/3).

Front

What is the relationship between radicals and rational exponents?

Back

Radicals can be expressed using rational exponents, where the nth root of a number can be written as that number raised to the power of 1/n.

Front

How do you simplify the expression 4^(1/3) x 4^(4/3)?

Back

You can simplify it by adding the exponents: 4^(1/3 + 4/3) = 4^(5/3).

Front

What is the radical form of x^(2/3)?

Back

The radical form of x^(2/3) is ∛(x^2).

Front

How do you write the expression ∛(x^7) in exponential form?

Back

In exponential form, ∛(x^7) is written as x^(7/3).

Front

What is the general formula for converting a radical expression of the form ∛(a) to exponential form?

Back

The general formula is a^(1/3), where 'a' is the expression under the radical.

Front

What is the product rule for exponents?

Back

The product rule states that when multiplying two expressions with the same base, you add the exponents: a^m * a^n = a^(m+n).

Front

What is the power of a power rule for exponents?

Back

The power of a power rule states that when raising an exponent to another exponent, you multiply the exponents: (a^m)^n = a^(m*n).