Algebra Examples

${(5^{3} \cdot 2^{4})}^{2} (5^{- 2} \cdot 2^{5})$

Step 1

Raise $5$ to the power of $3$ .

${(125 \cdot 2^{4})}^{2} (5^{- 2} \cdot 2^{5})$

Step 2

Raise $2$ to the power of $4$ .

${(125 \cdot 16)}^{2} (5^{- 2} \cdot 2^{5})$

Step 3

Multiply $125$ by $16$ .

$2000^{2} (5^{- 2} \cdot 2^{5})$

Step 4

Raise $2000$ to the power of $2$ .

$4000000 (5^{- 2} \cdot 2^{5})$

Step 5

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

$4000000 (\frac{1}{5^{2}} \cdot 2^{5})$

Step 6

Evaluate the exponents.

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Step 6.1

Raise $5$ to the power of $2$ .

$4000000 (\frac{1}{25} \cdot 2^{5})$

Step 6.2

Raise $2$ to the power of $5$ .

$4000000 (\frac{1}{25} \cdot 32)$

$4000000 (\frac{1}{25} \cdot 32)$

Step 7

Combine $\frac{1}{25}$ and $32$ .

$4000000 (\frac{32}{25})$

Step 8

Cancel the common factor of $25$ .

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Step 8.1

Factor $25$ out of $4000000$ .

$25 (160000) \frac{32}{25}$

Step 8.2

Cancel the common factor.

$25 \cdot 160000 \frac{32}{25}$

Step 8.3

Rewrite the expression.

$160000 \cdot 32$

$160000 \cdot 32$

Step 9

Multiply $160000$ by $32$ .

$5120000$

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