Understanding Rational Exponents and Radicals

The video tutorial explains how to simplify the expression 827 raised to the power of 2/3. It begins by applying the exponent to the numbers 8 and 27, converting the rational exponents into radical form. The tutorial then demonstrates how to simplify the cube roots of 8 and 27, using the fact that 8 is 2 cubed and 27 is 3 cubed. Finally, it calculates the result, showing that 827 raised to the power of 2/3 equals 4/9.

What is the first step in simplifying the expression 827 raised to the power of 2/3?

• Apply the exponent to both 8 and 27

• Convert the expression to a fraction

• Find the square root of 827

• Multiply 827 by 2/3

In a rational exponent, what does the denominator indicate?

• The exponent of the radical

• The index of the radical

• The base of the exponent

• The coefficient of the expression

How can 8 raised to the power of 2/3 be expressed in radical form?

• As the square root of the cube of 8

• As the square of the cube root of 8

• As the cube root of the square of 8

• As the cube of the square root of 8

What is the cube root of 8?

• 1

• 2

• 3

• 4

After finding the cube roots of 8 and 27, what is the next step in simplifying the expression?

• Multiply the results

• Add the results

• Square the results

• Divide the results