Basic Math Examples

${(2^{- 29} \cdot 8^{10} \cdot 2)}^{5}$

Step 1

Multiply $2^{- 29}$ by $2$ by adding the exponents.

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Step 1.1

Move $2$ .

${(2 \cdot 2^{- 29} \cdot 8^{10})}^{5}$

Step 1.2

Multiply $2$ by $2^{- 29}$ .

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Step 1.2.1

Raise $2$ to the power of $1$ .

${(2^{1} \cdot 2^{- 29} \cdot 8^{10})}^{5}$

Step 1.2.2

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

${(2^{1 - 29} \cdot 8^{10})}^{5}$

Step 1.3

Subtract $29$ from $1$ .

${(2^{- 28} \cdot 8^{10})}^{5}$

Step 2

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

${(\frac{1}{2^{28}} \cdot 8^{10})}^{5}$

Step 3

Evaluate the exponents.

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Step 3.1

Raise $2$ to the power of $28$ .

${(\frac{1}{268435456} \cdot 8^{10})}^{5}$

Step 3.2

Raise $8$ to the power of $10$ .

${(\frac{1}{268435456} \cdot 1073741824)}^{5}$

Step 4

Cancel the common factor of $268435456$ .

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Step 4.1

Factor $268435456$ out of $1073741824$ .

${(\frac{1}{268435456} \cdot (268435456 (4)))}^{5}$

Step 4.2

Cancel the common factor.

${(\frac{1}{268435456} \cdot (268435456 \cdot 4))}^{5}$

Step 4.3

Rewrite the expression.

$4^{5}$

Step 5

Raise $4$ to the power of $5$ .

$1024$