Basic Math Examples

\frac{{2.88}^{\frac{1}{2}}}{2^{\frac{1}{2}}} \div {(0.09)}^{\frac{3}{2}}

$\frac{{2.88}^{\frac{1}{2}}}{2^{\frac{1}{2}}} \div {(0.09)}^{\frac{3}{2}}$

Step 1

Rewrite the division as a fraction.

\frac{\frac{{2.88}^{\frac{1}{2}}}{2^{\frac{1}{2}}}}{{(0.09)}^{\frac{3}{2}}}

$\frac{\frac{{2.88}^{\frac{1}{2}}}{2^{\frac{1}{2}}}}{{(0.09)}^{\frac{3}{2}}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

\frac{{2.88}^{\frac{1}{2}}}{2^{\frac{1}{2}}} \cdot \frac{1}{{0.09}^{\frac{3}{2}}}

$\frac{{2.88}^{\frac{1}{2}}}{2^{\frac{1}{2}}} \cdot \frac{1}{{0.09}^{\frac{3}{2}}}$

Step 3

Combine fractions.

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Step 3.1

Combine.

\frac{{2.88}^{\frac{1}{2}} \cdot 1}{2^{\frac{1}{2}} \cdot {0.09}^{\frac{3}{2}}}

$\frac{{2.88}^{\frac{1}{2}} \cdot 1}{2^{\frac{1}{2}} \cdot {0.09}^{\frac{3}{2}}}$

Step 3.2

Multiply

{2.88}^{\frac{1}{2}}

${2.88}^{\frac{1}{2}}$ by

1

$1$ .

\frac{{2.88}^{\frac{1}{2}}}{2^{\frac{1}{2}} \cdot {0.09}^{\frac{3}{2}}}

$\frac{{2.88}^{\frac{1}{2}}}{2^{\frac{1}{2}} \cdot {0.09}^{\frac{3}{2}}}$

\frac{{2.88}^{\frac{1}{2}}}{2^{\frac{1}{2}} \cdot {0.09}^{\frac{3}{2}}}

$\frac{{2.88}^{\frac{1}{2}}}{2^{\frac{1}{2}} \cdot {0.09}^{\frac{3}{2}}}$

Step 4

Simplify the denominator.

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Step 4.1

Rewrite

0.09

$0.09$ as

{0.3}^{2}

${0.3}^{2}$ .

\frac{{2.88}^{\frac{1}{2}}}{2^{\frac{1}{2}} \cdot {({0.3}^{2})}^{\frac{3}{2}}}

$\frac{{2.88}^{\frac{1}{2}}}{2^{\frac{1}{2}} \cdot {({0.3}^{2})}^{\frac{3}{2}}}$

Step 4.2

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

\frac{{2.88}^{\frac{1}{2}}}{2^{\frac{1}{2}} \cdot {0.3}^{2 (\frac{3}{2})}}

$\frac{{2.88}^{\frac{1}{2}}}{2^{\frac{1}{2}} \cdot {0.3}^{2 (\frac{3}{2})}}$

Step 4.3

Cancel the common factor of

2

$2$ .

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Step 4.3.1

Cancel the common factor.

$\frac{{2.88}^{\frac{1}{2}}}{2^{\frac{1}{2}} \cdot {0.3}^{2 (\frac{3}{2})}}$

Step 4.3.2

Rewrite the expression.

$\frac{{2.88}^{\frac{1}{2}}}{2^{\frac{1}{2}} \cdot {0.3}^{3}}$

Step 4.4

Raise

$0.3$ to the power of

$3$ .

$\frac{{2.88}^{\frac{1}{2}}}{2^{\frac{1}{2}} \cdot 0.027}$

Step 5

Simplify the numerator.

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Step 5.1

Rewrite

$2.88$ as

${1.69705627}^{2}$ .

$\frac{{({1.69705627}^{2})}^{\frac{1}{2}}}{2^{\frac{1}{2}} \cdot 0.027}$

Step 5.2

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

$\frac{{1.69705627}^{2 (\frac{1}{2})}}{2^{\frac{1}{2}} \cdot 0.027}$

Step 5.3

Cancel the common factor of

$2$ .

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Step 5.3.1

Cancel the common factor.

$\frac{{1.69705627}^{2 (\frac{1}{2})}}{2^{\frac{1}{2}} \cdot 0.027}$

Step 5.3.2

Rewrite the expression.

$\frac{{1.69705627}^{1}}{2^{\frac{1}{2}} \cdot 0.027}$

Step 5.4

Evaluate the exponent.

$\frac{1.69705627}{2^{\frac{1}{2}} \cdot 0.027}$

Step 6

Simplify by multiplying terms.

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Step 6.1

Multiply

$2^{\frac{1}{2}}$ by

$0.027$ .

$\frac{1.69705627}{0.03818376}$

Step 6.2

Divide

$1.69705627$ by

$0.03818376$ .

$44.44444444$