Task Sets: Explain rational exponents - Common Core Math - HS Number and Quantity

Warm-Up: Integer Exponent Rules

These problems review skills you already know.

The power rule states that $(a^m)^n = a^{mn}$ . Applying this rule to $(5^{1/3})^3$ gives $5^{(1/3) \cdot 3} = 5^1 = 5$ . Which conclusion follows?

$5^{1/3}$ must be the number whose cube is 5, so $5^{1/3} = \sqrt[3]{5}$

$5^{1/3}$ must equal $\frac{5}{3}$ , since the exponent denominator is 3

$5^{1/3}$ must equal $\frac{1}{5^3}$ , since fractional exponents produce reciprocals

$5^{1/3}$ must equal $5^3$ , since roots and powers are inverse operations

Which statement correctly converts between radical and exponential notation?

$\sqrt[4]{x} = x^4$

$\sqrt[4]{x} = x^{1/4}$

$\sqrt[4]{x} = 4x$

$\sqrt[4]{x} = x^{-4}$

The product rule states $a^m \cdot a^n = a^{m+n}$ . Simplify $4^{1/2} \cdot 4^{3/2}$ using this rule. Show each step and state which rule you used.

Evaluate each expression.

What is the value of $8^{1/3}$ ?

$\frac{8}{3}$

$2$

$24$

$\sqrt{8}$

Evaluate $16^{3/4}$ .

Evaluate $27^{2/3}$ .

Simplify $27^{2/3} \div 27^{1/3}$ using the quotient rule $a^r \div a^s = a^{r-s}$ . Give a whole number answer.

Evaluate $8^{-2/3}$ . Express your answer as a fraction.