Fractional Powers and Radicals

• it disappears

Simplify:

• 2

• 4

• 16

• 64

Write in exponential form

∛x⁷

• x⁷∕ ³

• x3⁄7

• 3x⁷

• 7x³

Write in exponential form

√x⁵

• X¹∕ ⁵

• X ²⁄⁵

• X⁵⁄ ²

• X⁵

Is the result rational or irrational? Explain.

• Rational; The sum of two rationals is always rational.

• Sometimes rational, sometimes irrational; The sum of two irrationals is sometimes rational, sometimes irrational.

• Rational; The product of two rationals is always rational.

• Sometimes rational, sometimes irrational; The product of two irrationals is sometimes rational, sometimes irrational

Perform the operation.  Express your answer in simplest form.

• 54√14 - 12√33

• 18√14 - 6√33

• -3√6

• 3√14 - 2√33

• A
• B
• C
• D

Is the result rational or irrational? Explain.

• Rational; The sum of two rationals is always rational.

• Irrational; The sum of a rational and an irrational is always irrational.

• Rational; The product of two rationals is always rational.

• Irrational; The product of a nonzero rational and an irrational is always irrational.

Is the result rational or irrational? Explain.

• Rational; The sum of two rationals is always rational.

• Irrational; The sum of a rational and an irrational is always irrational.

• Rational; The product of two rationals is always rational.

• Sometimes rational, sometimes irrational; The product of two irrationals is sometimes rational, sometimes irrational

Rewrite x^3/4 in radical form

• ³√(x)⁴

• ⁴√(x)³

• ^x√(3)⁴

• 1/(³√(x)⁴)