Solved on Oct 30, 2023

Simplify $100^{3/2}$ and verify the result using a calculator.

STEP 1

Assumptions1. We need to simplify the expression $100^{\frac{3}{}}$ . . 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 $100^{\frac{}{2}}$ is in exponential form. We can convert it to radical form using the rule $a^{\frac{m}{n}} = \sqrt[n]{a^m}$ .
100^{\frac{}{2}} = \sqrt[2]{100^}

STEP 3

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

STEP 4

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

STEP 5

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

STEP 6

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

STEP 7

So, $100^{\frac{3}{2}} =10^3$ .
Now, we can calculate the value of $10^3$ .

STEP 8

Calculate the value of $10^3$ .
$10^3 =1000$ So, $100^{\frac{3}{2}} =1000$ .

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Simplify $100^{3/2}$ and verify the result using a calculator.

STEP 1

Assumptions1. We need to simplify the expression $100^{\frac{3}{}}$ . . 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 $100^{\frac{}{2}}$ is in exponential form. We can convert it to radical form using the rule $a^{\frac{m}{n}} = \sqrt[n]{a^m}$ .
100^{\frac{}{2}} = \sqrt[2]{100^}

STEP 3

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

STEP 4

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

STEP 5

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

STEP 6

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

STEP 7

So, $100^{\frac{3}{2}} =10^3$ .
Now, we can calculate the value of $10^3$ .

STEP 8

Calculate the value of $10^3$ .
$10^3 =1000$ So, $100^{\frac{3}{2}} =1000$ .

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

STEP 1

Assumptions1. We need to simplify the expression 1003100^{\frac{3}{}}1003​. . 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}}1002​ is in exponential form. We can convert it to radical form using the rule amn=amna^{\frac{m}{n}} = \sqrt[n]{a^m}anm​=nam​.100^{\frac{}{2}} = \sqrt[2]{100^}

STEP 3

We know that the square root of 100100100 is 101010, so we can simplify the expression further.10032=(102)32\sqrt[2]{100^3} = \sqrt[2]{(10^2)^3}21003​=2(102)3​

STEP 4

Using the rule of exponents (am)n=amn(a^m)^n = a^{mn}(am)n=amn, we can simplify the expression further.(102)32=102×32\sqrt[2]{(10^2)^3} = \sqrt[2]{10^{2 \times3}}2(102)3​=2102×3​

STEP 5

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

STEP 6

The square root of 10610^6106 is 10310^3103, so we can simplify the expression to its final form.1062=103\sqrt[2]{10^6} =10^32106​=103

STEP 7

So, 10032=103100^{\frac{3}{2}} =10^310023​=103.Now, we can calculate the value of 10310^3103.

STEP 8

Calculate the value of 10310^3103.103=100010^3 =1000103=1000So, 10032=1000100^{\frac{3}{2}} =100010023​=1000.

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Simplify $100^{3/2}$ and verify the result using a calculator.

Assumptions1. We need to simplify the expression $100^{\frac{3}{}}$ . . We need to write the expression in radical form before simplifying.
3. We can use a calculator if necessary to verify our answer.

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

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

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

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

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

So, $100^{\frac{3}{2}} =10^3$ .
Now, we can calculate the value of $10^3$ .

Calculate the value of $10^3$ .
$10^3 =1000$ So, $100^{\frac{3}{2}} =1000$ .