Exponents I&E

How many nth roots and what type will the expression have? n=3, a=-216

• One real nth root

• Two real nth roots

• No real nth roots

• Positive

• Negative

Answer explanation

An odd index and a negative base means there is one output that is negative.

Find the indicated real nth root(s) of a n=3, a=-216

Mathematical Equivalence

ON

How many nth roots and what type will the expression have? n=4, a=1

• One real nth root

• Two real nth roots

• No real nth roots

• Positive

• Negative

Answer explanation

An even index and a positive base means there will always be two outputs, one positive and one negative.

Find the indicated real nth root(s) of a n=4, a=1

Mathematical Equivalence

ON

How many nth roots and what type will the expression have? n=3, a=218

• One real nth root

• Two real nth roots

• No real nth roots

• Positive

• Negative

Answer explanation

An odd index and a positive base will give you one output that is positive.

Find the indicated real nth root(s) of a n=3, a=218

Mathematical Equivalence

ON

How many nth roots and what type will the expression have? n=6, a=-7776

• One real nth root

• Two real nth roots

• No real nth roots

• Positive

• Negative

Answer explanation

An even index and a negative base will have no REAL nth roots and therefore no real outputs.

How many nth roots and what type will the expression have? n=8, a=0

• One real nth root

• Two real nth roots

• No real nth roots

• Positive

• Negative

Answer explanation

A base of 0 will always give one output of 0 no matter what the index is.

Find the indicated real nth root(s) of a n=8, a=0

Mathematical Equivalence

ON

Mathematical Equivalence

OFF