Writing Equivalent Radical and Rational Exponent Expressions

This lesson covers how to write equivalent radical and rational exponent expressions using properties of rational exponents. It explains the relationship between radicals and rational exponents, how to combine exponents, and the process of simplifying radicals. The lesson also demonstrates converting radicals to fractional exponents and vice versa, emphasizing the importance of common denominators when adding exponents. By the end, students will understand how to simplify expressions using both integer exponents and radicals.

What is the relationship between the index of a radical and the denominator of a rational exponent?

• The index is the base of the rational exponent.

• The index is unrelated to the rational exponent.

• The index is the denominator of the rational exponent.

• The index is the numerator of the rational exponent.

When simplifying expressions, what must be true about the bases to combine exponents?

• The bases must be the same.

• The bases must be different.

• The bases must be fractions.

• The bases must be integers.

How do you simplify a radical expression with a radicand that has an exponent?

• The exponent becomes the index of the radical.

• The exponent is ignored.

• The exponent becomes the numerator of the rational exponent.

• The exponent is added to the index.

What is the first step in converting a radical expression to a rational exponent?

• Multiply the exponents.

• Subtract the exponents.

• Turn the radical into a fraction.

• Add the exponents.

When combining like bases with fractional exponents, what must you do before adding the exponents?

• Find a common numerator.

• Find a common denominator.

• Multiply the exponents.

• Divide the exponents.

In the expression 3 times x to the 7/3 times y to the 14/3, what is the process to convert it back to a radical form?

• Decompose the exponents into fractions that give integers.

• Add the exponents together.

• Multiply the exponents by 3.

• Subtract the exponents from each other.

What is the result of simplifying the expression 3 times x squared y to the 4th times the cube root of xy squared?

• 3 times x to the 6/3 y to the 12/3

• 3 times x to the 6th y to the 12th

• 3 times x to the 1/3 y to the 2/3

• 3 times x squared y to the 4th