Question

lesson 5 topic review name: period: lesson 5.1 nth root, radicals and rational exponents what is the value of each expression? rounded to the nearest hundredth, if necessary. 1) 2) simplify each expression. assume all variables are positive. 3) 4) solve each equation. 5) 750 = 6y³ lesson 5.2 properties of exponents and radicals what is the reduced radical form of each expression? assume all variables are positive. 6) 7) multiply. 8) (9x + √2) (9x - √2) 9) ³√4(8 ³√2 - 1) rewrite rational expression to radical expression and vice versa. 10) 3^(3/4) 11) 3^(7/10)a^(2/3) 12) (⁵√a)⁴ 13) (⁶√x)⁵ lesson 5.3 properties of exponents and radicals graph the following functions. what are the domain and range? is the function increasing or de 14) f(x) = √(x - 1) 15) f(x) = ³√(x + 2) domain: increasing or decreasing? domain: increa range:

Explanation:

Let's solve question 1: \( \sqrt[4]{16^3} \)

Step 1: Simplify the base inside the radical

First, calculate \( 16^3 \). We know that \( 16 = 2^4 \), so \( 16^3=(2^4)^3 = 2^{12} \) (using the power - of - a - power rule \((a^m)^n=a^{mn}\)). So the expression becomes \( \sqrt[4]{2^{12}} \)

Step 2: Use the property of radicals

The property of radicals states that \( \sqrt[n]{a^m}=a^{\frac{m}{n}} \) (when \( a\geq0 \) for even \( n \)). For \( \sqrt[4]{2^{12}} \), where \( n = 4 \) and \( m=12 \), we have \( 2^{\frac{12}{4}} \)

Step 3: Simplify the exponent

Simplify \( \frac{12}{4}=3 \). So \( 2^{3}=8 \)

Answer:

The value of \( \sqrt[4]{16^3} \) is \( 8 \)