Exponent Rules

Question 1

What do you do when an exponent is raised to another exponent? e.g. (x^2)^3?

Answer 1

Multiply the two exponents. x^2*3=x^6

Question 2

Can you combine variables with different exponents?

Answer 2

No. x^3 + x^2 cannot be combined.

Question 3

How do you add two variables with the same exponent?

Answer 3

2x^2 + 5x^2= 7x^2.

Question 4

If like bases are being multiplied (e.g. x * x^3), what do you do with the exponents?

Answer 4

Add the exponents. e.g. x * x^3 = x^4.

Question 5

Can you add the exponents of like bases being added?

Answer 5

No. x^3 + x^4 does not equal x^7.

Question 6

In a polynomial, should variables with exponents be written in ascending or descending order?

Answer 6

Descending order. e.g. x^3 + x^2 + x.

Question 7

If you have a fraction with the same base on the top and bottom, how can you simplify?

Answer 7

Subtract the exponents. e.g. (x^4) / (x) means (x^4)(x^-1) = x^(4-1) = x^3