Basic Math Examples

$10^{16 {(6.77 \cdot 10^{6})}^{- 3}}$

Step 1

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

$10^{16 \frac{1}{{(6.77 \cdot 10^{6})}^{3}}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $6.77 \cdot 10^{6}$ .

$10^{16 \frac{1}{{6.77}^{3} \cdot {(10^{6})}^{3}}}$

Step 2.2

Raise $6.77$ to the power of $3$ .

$10^{16 \frac{1}{310.288733 \cdot {(10^{6})}^{3}}}$

Step 2.3

Multiply the exponents in ${(10^{6})}^{3}$ .

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Step 2.3.1

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

$10^{16 \frac{1}{310.288733 \cdot 10^{6 \cdot 3}}}$

Step 2.3.2

Multiply $6$ by $3$ .

$10^{16 \frac{1}{310.288733 \cdot 10^{18}}}$

Step 2.4

Raise $10$ to the power of $18$ .

$10^{16 \frac{1}{310.288733 \cdot 1000000000000000000}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Multiply $310.288733$ by $1000000000000000000$ .

$10^{16 (\frac{1}{310288733000000000000})}$

Step 3.2

Cancel the common factor of $16$ .

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Step 3.2.1

Factor $16$ out of $310288733000000000000$ .

$10^{16 \frac{1}{16 (19393045812500000000)}}$

Step 3.2.2

Cancel the common factor.

$10^{16 \frac{1}{16 \cdot 19393045812500000000}}$

Step 3.2.3

Rewrite the expression.

$10^{\frac{1}{19393045812500000000}}$

Step 3.3

Simplify the expression.

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Step 3.3.1

Divide $1$ by $19393045812500000000$ .

$10^{0}$

Step 3.3.2

Raise $10$ to the power of $0$ .

$1$