Answer:
To rewrite (100^{7/2}) in radical form, you can use the property of exponents that states: (a^{m/n} = \sqrt[n]{a^m}).
So, (100^{7/2}) can be rewritten as: 1007
This is the radical form of (100^{7/2}).
Step-by-step explanation:
Let’s break down the process of rewriting (100^{7/2}) in radical form step by step:
1. Understand the Exponent Rule:
The expression: (a^{m/n})
can be rewritten as: (\sqrt[n]{a^m}).
This means that the exponent (m/n) indicates a radical
(root) form.
2. Identify the Base and Exponents:
In (100^{7/2}): the base is 100,
the numerator of the exponent is 7; and
the denominator is 2.
3. Apply the Exponent Rule:
Using the rule (a^{m/n} = \sqrt[n]{a^m}), rewrite
(100^{7/2}) as:
[ 100^{7/2} = \sqrt[2]{100^7} ]
4. Simplify the Radical:
The square root (denoted by (\sqrt{})) is the same
as the 2nd root, so we can simplify the expression to:
[ \sqrt{100^7} ] , So
100^{7/2}) in radical form is (\sqrt{100^7}).