Basic Math Examples

${((4^{- 15}) (2^{6}))}^{3}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{1}{4^{15}} \cdot 2^{6})}^{3}$

Step 2

Evaluate the exponents.

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Step 2.1

Raise $4$ to the power of $15$ .

${(\frac{1}{1073741824} \cdot 2^{6})}^{3}$

Step 2.2

Raise $2$ to the power of $6$ .

${(\frac{1}{1073741824} \cdot 64)}^{3}$

${(\frac{1}{1073741824} \cdot 64)}^{3}$

Step 3

Cancel the common factor of $64$ .

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Step 3.1

Factor $64$ out of $1073741824$ .

${(\frac{1}{64 (16777216)} \cdot 64)}^{3}$

Step 3.2

Cancel the common factor.

${(\frac{1}{64 \cdot 16777216} \cdot 64)}^{3}$

Step 3.3

Rewrite the expression.

${(\frac{1}{16777216})}^{3}$

${(\frac{1}{16777216})}^{3}$

Step 4

Simplify the expression.

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Step 4.1

Apply the product rule to $\frac{1}{16777216}$ .

$\frac{1^{3}}{16777216^{3}}$

Step 4.2

One to any power is one.

$\frac{1}{16777216^{3}}$

Step 4.3

Raise $16777216$ to the power of $3$ .

$\frac{1}{4722366482869640000000}$

$\frac{1}{4722366482869640000000}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{4722366482869640000000}$

Decimal Form:

$2.11758236 \cdot 10^{- 22}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$