Math  /  Algebra

Question6. Copy and complete the table. Express values in the last column in rational form. a) b) c) d) \begin{tabular}{|c|c|l|} \hline \begin{tabular}{l} Exponential \\ Form \end{tabular} & Radical Form & \begin{tabular}{l} Evaluation \\ of Expression \end{tabular} \\ \hline 10012100^{\frac{1}{2}} & & \\ \hline 160.2516^{0.25} & & \\ \hline & 121\sqrt{121} & \\ \hline(27)53(-27)^{\frac{5}{3}} & & \\ \hline 492.549^{2.5} & & \\ \hline & 102410\sqrt[10]{1024} & \\ \hline \end{tabular}

Studdy Solution

STEP 1

1. The table contains exponential and radical forms of expressions, and we need to evaluate them.
2. The goal is to express the evaluations in rational form.

STEP 2

1. Convert exponential forms to radical forms.
2. Convert radical forms to exponential forms.
3. Evaluate each expression and express the result in rational form.

STEP 3

Convert 10012 100^{\frac{1}{2}} to radical form: 10012=100 100^{\frac{1}{2}} = \sqrt{100}

STEP 4

Convert 160.25 16^{0.25} to radical form: 160.25=1614=164 16^{0.25} = 16^{\frac{1}{4}} = \sqrt[4]{16}

STEP 5

Convert 121\sqrt{121} to exponential form: 121=12112 \sqrt{121} = 121^{\frac{1}{2}}

STEP 6

Convert (27)53(-27)^{\frac{5}{3}} to radical form: (27)53=(273)5 (-27)^{\frac{5}{3}} = \left(\sqrt[3]{-27}\right)^5

STEP 7

Convert 492.549^{2.5} to radical form: 492.5=4952=(49)5 49^{2.5} = 49^{\frac{5}{2}} = \left(\sqrt{49}\right)^5

STEP 8

Convert 102410\sqrt[10]{1024} to exponential form: 102410=1024110 \sqrt[10]{1024} = 1024^{\frac{1}{10}}

STEP 9

Evaluate 10012=100=10 100^{\frac{1}{2}} = \sqrt{100} = 10

STEP 10

Evaluate 160.25=164=2 16^{0.25} = \sqrt[4]{16} = 2

STEP 11

Evaluate 121=11\sqrt{121} = 11

STEP 12

Evaluate (27)53=(273)5=(3)5=243(-27)^{\frac{5}{3}} = \left(\sqrt[3]{-27}\right)^5 = (-3)^5 = -243

STEP 13

Evaluate 492.5=(49)5=75=1680749^{2.5} = \left(\sqrt{49}\right)^5 = 7^5 = 16807

STEP 14

Evaluate 102410=1024110=2\sqrt[10]{1024} = 1024^{\frac{1}{10}} = 2
The completed table is:
\begin{tabular}{|c|c|l|} \hline \begin{tabular}{l} Exponential \\ Form \end{tabular} & Radical Form & \begin{tabular}{l} Evaluation \\ of Expression \end{tabular} \\ \hline 100^{\frac{1}{2}} & \sqrt{100} & 10 \\ \hline 16^{0.25} & \sqrt[4]{16} & 2 \\ \hline 121^{\frac{1}{2}} & \sqrt{121} & 11 \\ \hline (-27)^{\frac{5}{3}} & \left(\sqrt[3]{-27}\right)^5 & -243 \\ \hline 49^{2.5} & \left(\sqrt{49}\right)^5 & 16807 \\ \hline 1024^{\frac{1}{10}} & \sqrt[10]{1024} & 2 \\ \hline \end{tabular}

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