Basic Math Examples

$(\frac{7}{3^{10}}) (\frac{8}{5^{- 7}}) (\frac{7}{3^{23}}) (\frac{8}{5^{7}})$

Step 1

Combine fractions.

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Step 1.1

Raise $5$ to the power of $7$ .

$(\frac{7}{3^{10}}) (\frac{8}{5^{- 7}}) \cdot (\frac{7}{3^{23}}) \cdot \frac{8}{78125}$

Step 1.2

Raise $3$ to the power of $23$ .

$(\frac{7}{3^{10}}) (\frac{8}{5^{- 7}}) \cdot \frac{7}{94143178827} \cdot \frac{8}{78125}$

Step 1.3

Combine.

$\frac{7 \cdot 8}{3^{10} \cdot 5^{- 7}} \cdot \frac{7}{94143178827} \cdot \frac{8}{78125}$

Step 1.4

Combine.

$\frac{7 \cdot 8 \cdot 7}{3^{10} \cdot 5^{- 7} \cdot 94143178827} \cdot \frac{8}{78125}$

Step 1.5

Combine.

$\frac{7 \cdot 8 \cdot 7 \cdot 8}{3^{10} \cdot 5^{- 7} \cdot 94143178827 \cdot 78125}$

Step 1.6

Move $5^{- 7}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{7 \cdot 8 \cdot 7 \cdot 8 \cdot 5^{7}}{3^{10} \cdot 94143178827 \cdot 78125}$

Step 2

Simplify the numerator.

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Step 2.1

Multiply $7$ by $8$ .

$\frac{56 \cdot 7 \cdot 8 \cdot 5^{7}}{3^{10} \cdot 94143178827 \cdot 78125}$

Step 2.2

Multiply $56$ by $7$ .

$\frac{392 \cdot 8 \cdot 5^{7}}{3^{10} \cdot 94143178827 \cdot 78125}$

Step 2.3

Multiply $392$ by $8$ .

$\frac{3136 \cdot 5^{7}}{3^{10} \cdot 94143178827 \cdot 78125}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite $94143178827$ as $3^{23}$ .

$\frac{3136 \cdot 5^{7}}{3^{10} \cdot 3^{23} \cdot 78125}$

Step 3.2

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

$\frac{3136 \cdot 5^{7}}{3^{10 + 23} \cdot 78125}$

Step 3.3

Add $10$ and $23$ .

$\frac{3136 \cdot 5^{7}}{3^{33} \cdot 78125}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Raise $5$ to the power of $7$ .

$\frac{3136 \cdot 78125}{3^{33} \cdot 78125}$

Step 4.2

Simplify the expression.

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Step 4.2.1

Raise $3$ to the power of $33$ .

$\frac{3136 \cdot 78125}{5559060566555520 \cdot 78125}$

Step 4.2.2

Multiply $3136$ by $78125$ .

$\frac{245000000}{5559060566555520 \cdot 78125}$

Step 4.2.3

Multiply $5559060566555520$ by $78125$ .

$\frac{245000000}{434301606762150000000}$

Step 4.3

Cancel the common factor of $245000000$ and $434301606762150000000$ .

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Step 4.3.1

Factor $5000000$ out of $245000000$ .

$\frac{5000000 (49)}{434301606762150000000}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $5000000$ out of $434301606762150000000$ .

$\frac{5000000 \cdot 49}{5000000 \cdot 86860321352430}$

Step 4.3.2.2

Cancel the common factor.

$\frac{5000000 \cdot 49}{5000000 \cdot 86860321352430}$

Step 4.3.2.3

Rewrite the expression.

$\frac{49}{86860321352430}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{49}{86860321352430}$

Decimal Form:

$5.64124092 \cdot 10^{- 13}$