The radical expressions and their corresponding expression in rational exponent form are
[tex]972^\frac 15 = 3\sqrt[5]{4}[/tex], [tex]448^\frac 13 = 4\sqrt[3]{7}[/tex], [tex]3528^\frac 12 = 42 \sqrt 2[/tex] and [tex]4050^\frac 14 = 3\sqrt[4]{50}[/tex]
How to match the tiles?
We start by evaluating each expression as follows:
[tex]972^\frac 15[/tex]
Expand 972
[tex]972^\frac 15 = (243 * 3)^\frac 15[/tex]
Take the 5th root of 243
[tex]972^\frac 15 = 3* (4)^\frac 15[/tex]
Rewrite as:
[tex]972^\frac 15 = 3\sqrt[5]{4}[/tex]
Next, we have:
[tex]448^\frac 13[/tex]
Expand 448
[tex]448^\frac 13 = (64 * 7)^\frac 13[/tex]
Take the 3rd root of 64
[tex]448^\frac 13 = 4 * (7)^\frac 13[/tex]
Rewrite as:
[tex]448^\frac 13 = 4\sqrt[3]{7}[/tex]
Next, we have:
[tex]3528^\frac 12[/tex]
Expand 3528
[tex]3528^\frac 12 = (1764 * 2)^\frac 12[/tex]
Take the square root of 1764
[tex]3528^\frac 12 = 42 * (2)^\frac 12[/tex]
Rewrite as:
[tex]3528^\frac 12 = 42 \sqrt 2[/tex]
Lastly, we have:
[tex]4050^\frac 14[/tex]
Expand 4050
[tex]4050^\frac 14 = (81 * 50)^\frac 14[/tex]
Take the 4th root of 81
[tex]4050^\frac 14 = 3 (50)^\frac 14[/tex]
Rewrite as:
[tex]4050^\frac 14 = 3\sqrt[4]{50}[/tex]
Read more about radical expressions at:
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