Exponents and Roots Simplification

The video tutorial covers simplifying mathematical expressions involving roots and exponents. It begins with calculating the cubed root of 27 raised to the fourth power, followed by finding the square root of 148 cubed. The tutorial then addresses handling negative exponents using 64 and concludes with simplifying expressions involving powers of powers. Each section provides step-by-step explanations and calculations, emphasizing the importance of making exponents positive and rounding results appropriately.

What is the first step in simplifying the expression involving the cube root of 27 raised to the fourth power?

• Divide 27 by 3

• Multiply 27 by 4

• Find the cube root of 27

• Find the fourth power of 27

What is the result of three to the fourth power?

• 9

• 64

• 81

• 27

What is the cube root of 27?

• 9

• 6

• 3

• 12

How is the square root of 148 cubed expressed as a fractional exponent?

• 148 to the power of 1/2

• 148 to the power of 3/2

• 148 to the power of 3

• 148 to the power of 2/3

What is the result of 148 to the power of 3/2 when calculated?

• 1480.5

• 180.5

• 148.5

• 1800.5

What is the purpose of rewriting expressions with fractional exponents?

• To make calculations easier

• To increase the value

• To change the base

• To decrease the value

What is the first step in simplifying 1 over 64 to the negative one-third?

• Subtract 64 from the denominator

• Flip the fraction to make the exponent positive

• Multiply by 64

• Add 64 to the numerator

What is 64 to the power of one-third?

• 8

• 2

• 16

• 4

What is the result of 4 times 4 times 4?

• 16

• 64

• 32

• 8

What is the result of 64 to the negative one-third if not simplified?

• 1/16

• 1/64

• 1/4

• 1/8