Exploring Properties of Exponents and Radicals

This video tutorial covers properties of exponents and radicals, including how to rewrite and simplify expressions using these properties. It provides examples of rewriting expressions with exponents, simplifying nth roots, handling products and quotients of radicals, adding and subtracting radicals, multiplying binomial radical expressions, and rationalizing denominators using conjugates.

What is the result when multiplying two expressions with the same base?

• Multiply the exponents

• Add the exponents

• Divide the exponents

• Subtract the exponents

How do you simplify 81^(5/6) * 81^(-1/3)?

• 81^(1/2)

• 81^(2/3)

• 81^(1/6)

• 81^(1/3)

How can the nth root of a product a*b be rewritten?

• nth root of a + nth root of b

• a^(1/n) * b^(1/n)

• a^(1/n) + b^(1/n)

• nth root of a * nth root of b

What is the simplified form of the cube root of 16x^5?

• 2x^2 * cube root of 2x

• 2x * cube root of x^2

• 2x * cube root of 2x^2

• 2x^2 * cube root of x

How do you rationalize the denominator of cube root of 2n / 9m?

• Multiply by cube root of 3m

• Multiply by cube root of 27m^3

• Multiply by cube root of 3m^2

• Multiply by cube root of 9m^2

What is the simplified form of 2 cube root of 7 - cube root of 343?

• 2 cube root of 7 - cube root of 49

• 2 cube root of 7 - 7

• 2 cube root of 7 - cube root of 7

• 2 cube root of 7 - 1

What is the result of multiplying 2x by -sqrt(3)?

• -2 sqrt(3)x

• 2 sqrt(3)

• 2 sqrt(3)x

• -2 sqrt(3)

How do you simplify the expression 2x * 2x?

• 2x^2

• 2x

• 4x^2

• 4x

What is the simplified form of 2 - sqrt(5) / 4 - 5?

• 2 + sqrt(5)

• -2 - sqrt(5)

• -2 + sqrt(5)

• 2 - sqrt(5)

What is the result of adding 2 sqrt(5) and -sqrt(5)?

• sqrt(5)

• 3 sqrt(5)

• 2 sqrt(5)

• 0