Math

Question Simplify 1003/2100^{3/2} and verify the result using a calculator.

Studdy Solution

STEP 1

Assumptions1. We need to simplify the expression 1003100^{\frac{3}{}}. . We need to write the expression in radical form before simplifying.
3. We can use a calculator if necessary to verify our answer.

STEP 2

The expression 1002100^{\frac{}{2}} is in exponential form. We can convert it to radical form using the rule amn=amna^{\frac{m}{n}} = \sqrt[n]{a^m}.
100^{\frac{}{2}} = \sqrt[2]{100^}

STEP 3

We know that the square root of 100100 is 1010, so we can simplify the expression further.
10032=(102)32\sqrt[2]{100^3} = \sqrt[2]{(10^2)^3}

STEP 4

Using the rule of exponents (am)n=amn(a^m)^n = a^{mn}, we can simplify the expression further.
(102)32=102×32\sqrt[2]{(10^2)^3} = \sqrt[2]{10^{2 \times3}}

STEP 5

implify the exponent.
\sqrt[2]{10^{2 \times3}} = \sqrt[2]{10^}

STEP 6

The square root of 10610^6 is 10310^3, so we can simplify the expression to its final form.
1062=103\sqrt[2]{10^6} =10^3

STEP 7

So, 10032=103100^{\frac{3}{2}} =10^3.
Now, we can calculate the value of 10310^3.

STEP 8

Calculate the value of 10310^3.
103=100010^3 =1000So, 10032=1000100^{\frac{3}{2}} =1000.

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