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How do you simplify #100^(-3/2)#?

Answer 1

Isaiah Anthony

See full explanation below:

First, we need to understand the following exponent rule:

#(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#

The reverse is also true:

#x^(color(red)(a) xx color(blue)(b)) = (x^color(red)(a))^color(blue)(b)#

We can modify this expression as follows using these rules:

#100^(-3/2) = 100^(color(red)(1/2) xx color(blue)(-3)) = (100^(1/2))^-3#

We can now simplify the term within parenthesis:

#(100^(1/2))^-3 = 10^-3#

Next we need to understand this rule for exponents:

#x^color(red)(a) = 1/x^color(red)(-a)#

Applying this rule to our problem gives:

#10^color(red)(-3) = 1/10^color(red)(- -3) = 1/10^color(red)(3) = 1/(10 xx 10 xx 10) = 1/1000# or #0.001#

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Answer 2

Avery Alexander

To simplify (100^{-\frac{3}{2}}), we use the property (a^{-n} = \frac{1}{a^n}). So, (100^{-\frac{3}{2}} = \frac{1}{100^{\frac{3}{2}}}). Next, we simplify (100^{\frac{3}{2}}). Since (100 = 10^2), (100^{\frac{3}{2}} = (10^2)^{\frac{3}{2}} = 10^{2 \times \frac{3}{2}} = 10^3). Therefore, (100^{-\frac{3}{2}} = \frac{1}{10^3} = \frac{1}{1000}).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.