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kotykmax [81]
3 years ago
7

HELP!!!In the expression 100 a/b, if a is greater than b, which statements are true? b ≠ 0. Select all that apply.

Mathematics
1 answer:
MAXImum [283]3 years ago
4 0

Answer:

\large\boxed{\text{The expression is equal to}\ \sqrt[b]{100^a}}\\\boxed{\text{The expression is greater than 100}}

Step-by-step explanation:

a^\frac{m}{n}=\sqrt[n]{a^m}\\\\\text{True statement:}\\\\100^\frac{a}{b}=\sqrt[b]{100^a}\\\\a>b\to\dfrac{a}{b}>1\to\dfrac{a}{b}=1\dfrac{a-b}{b}\\\\100^\frac{a}{b}=100^{1\frac{a-b}{b}}=100^{1+\frac{a-b}{b}}=100^1\cdot100^\frac{a-b}{b}=100\sqrt[b]{100^{a-b}}\\\\a>b\to a-b>0\to100^{a-b}>1\\\\\text{Therefore}\ 100\sqrt[b]{100^{a-b}}>100

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