Basic Math Examples

${(\frac{1}{4})}^{- 2} - 3 \cdot 8^{\frac{2}{3}} \cdot 4^{0 + \frac{9}{16}} - \frac{1}{2}$

Step 1

Simplify each term.

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Step 1.1

Change the sign of the exponent by rewriting the base as its reciprocal.

$4^{2} - 3 \cdot 8^{\frac{2}{3}} \cdot 4^{0 + \frac{9}{16}} - \frac{1}{2}$

Step 1.2

Raise $4$ to the power of $2$ .

$16 - 3 \cdot 8^{\frac{2}{3}} \cdot 4^{0 + \frac{9}{16}} - \frac{1}{2}$

Step 1.3

Rewrite $8$ as $2^{3}$ .

$16 - 3 \cdot {(2^{3})}^{\frac{2}{3}} \cdot 4^{0 + \frac{9}{16}} - \frac{1}{2}$

Step 1.4

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$16 - 3 \cdot 2^{3 (\frac{2}{3})} \cdot 4^{0 + \frac{9}{16}} - \frac{1}{2}$

Step 1.5

Cancel the common factor of $3$ .

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Step 1.5.1

Cancel the common factor.

$16 - 3 \cdot 2^{3 (\frac{2}{3})} \cdot 4^{0 + \frac{9}{16}} - \frac{1}{2}$

Step 1.5.2

Rewrite the expression.

$16 - 3 \cdot 2^{2} \cdot 4^{0 + \frac{9}{16}} - \frac{1}{2}$

Step 1.6

Raise $2$ to the power of $2$ .

$16 - 3 \cdot 4 \cdot 4^{0 + \frac{9}{16}} - \frac{1}{2}$

Step 1.7

Multiply $4$ by $4^{0 + \frac{9}{16}}$ by adding the exponents.

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Step 1.7.1

Move $4^{0 + \frac{9}{16}}$ .

$16 - 3 \cdot (4^{0 + \frac{9}{16}} \cdot 4) - \frac{1}{2}$

Step 1.7.2

Multiply $4^{0 + \frac{9}{16}}$ by $4$ .

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Step 1.7.2.1

Raise $4$ to the power of $1$ .

$16 - 3 \cdot (4^{0 + \frac{9}{16}} \cdot 4^{1}) - \frac{1}{2}$

Step 1.7.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$16 - 3 \cdot 4^{0 + \frac{9}{16} + 1} - \frac{1}{2}$

Step 1.7.3

Add $0$ and $\frac{9}{16}$ .

$16 - 3 \cdot 4^{\frac{9}{16} + 1} - \frac{1}{2}$

Step 1.7.4

Write $1$ as a fraction with a common denominator.

$16 - 3 \cdot 4^{\frac{9}{16} + \frac{16}{16}} - \frac{1}{2}$

Step 1.7.5

Combine the numerators over the common denominator.

$16 - 3 \cdot 4^{\frac{9 + 16}{16}} - \frac{1}{2}$

Step 1.7.6

Add $9$ and $16$ .

$16 - 3 \cdot 4^{\frac{25}{16}} - \frac{1}{2}$

Step 2

To write $16$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$16 \cdot \frac{2}{2} - \frac{1}{2} - 3 \cdot 4^{\frac{25}{16}}$

Step 3

Combine $16$ and $\frac{2}{2}$ .

$\frac{16 \cdot 2}{2} - \frac{1}{2} - 3 \cdot 4^{\frac{25}{16}}$

Step 4

Combine the numerators over the common denominator.

$\frac{16 \cdot 2 - 1}{2} - 3 \cdot 4^{\frac{25}{16}}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $16$ by $2$ .

$\frac{32 - 1}{2} - 3 \cdot 4^{\frac{25}{16}}$

Step 5.2

Subtract $1$ from $32$ .

$\frac{31}{2} - 3 \cdot 4^{\frac{25}{16}}$

Step 6

To write $- 3 \cdot 4^{\frac{25}{16}}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{31}{2} - 3 \cdot 4^{\frac{25}{16}} \cdot \frac{2}{2}$

Step 7

Combine $- 3 \cdot 4^{\frac{25}{16}}$ and $\frac{2}{2}$ .

$\frac{31}{2} + \frac{- 3 \cdot 4^{\frac{25}{16}} \cdot 2}{2}$

Step 8

Simplify the expression.

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Step 8.1

Combine the numerators over the common denominator.

$\frac{31 - 3 \cdot 4^{\frac{25}{16}} \cdot 2}{2}$

Step 8.2

Multiply $2$ by $- 3$ .

$\frac{31 - 6 \cdot 4^{\frac{25}{16}}}{2}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{31 - 6 \cdot 4^{\frac{25}{16}}}{2}$

Decimal Form:

$- 10.67218558 \dots$