Basic Math Examples

$2^{s} \cdot 4^{2 s} = \frac{1}{1024}$

Step 1

Raise $1024$ to the power of $1$ .

$2^{s} \cdot 4^{2 s} = \frac{1}{1024^{1}}$

Step 2

Move $1024^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$2^{s} \cdot 4^{2 s} = 1024^{- 1}$

Step 3

Rewrite $4$ as $2^{2}$ .

$2^{s} \cdot {(2^{2})}^{2 s} = 1024^{- 1}$

Step 4

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

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Step 4.1

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

$2^{s} \cdot 2^{2 (2 s)} = 1024^{- 1}$

Step 4.2

Multiply $2$ by $2$ .

$2^{s} \cdot 2^{4 s} = 1024^{- 1}$

Step 5

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

$2^{s + 4 s} = 1024^{- 1}$

Step 6

Add $s$ and $4 s$ .

$2^{5 s} = 1024^{- 1}$

Step 7

Create equivalent expressions in the equation that all have equal bases.

$2^{5 s} = 2^{- 10}$

Step 8

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$5 s = - 10$

Step 9

Divide each term in $5 s = - 10$ by $5$ and simplify.

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Step 9.1

Divide each term in $5 s = - 10$ by $5$ .

$\frac{5 s}{5} = \frac{- 10}{5}$

Step 9.2

Simplify the left side.

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Step 9.2.1

Cancel the common factor of $5$ .

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Step 9.2.1.1

Cancel the common factor.

$\frac{5 s}{5} = \frac{- 10}{5}$

Step 9.2.1.2

Divide $s$ by $1$ .

$s = \frac{- 10}{5}$

Step 9.3

Simplify the right side.

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Step 9.3.1

Divide $- 10$ by $5$ .

$s = - 2$