Basic Math Examples

${(4^{7})}^{3} \cdot {(4^{- 4})}^{2}$

Step 1

Multiply the exponents in ${(4^{7})}^{3}$ .

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Step 1.1

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

$4^{7 \cdot 3} \cdot {(4^{- 4})}^{2}$

Step 1.2

Multiply $7$ by $3$ .

$4^{21} \cdot {(4^{- 4})}^{2}$

Step 2

Raise $4$ to the power of $21$ .

$4398046511104 \cdot {(4^{- 4})}^{2}$

Step 3

Multiply the exponents in ${(4^{- 4})}^{2}$ .

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Step 3.1

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

$4398046511104 \cdot 4^{- 4 \cdot 2}$

Step 3.2

Multiply $- 4$ by $2$ .

$4398046511104 \cdot 4^{- 8}$

Step 4

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

$4398046511104 \cdot \frac{1}{4^{8}}$

Step 5

Raise $4$ to the power of $8$ .

$4398046511104 \cdot \frac{1}{65536}$

Step 6

Cancel the common factor of $65536$ .

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Step 6.1

Factor $65536$ out of $4398046511104$ .

$65536 (67108864) \cdot \frac{1}{65536}$

Step 6.2

Cancel the common factor.

$65536 \cdot 67108864 \cdot \frac{1}{65536}$

Step 6.3

Rewrite the expression.

$67108864$