Algebra Examples

${(10^{\frac{3}{4}} \cdot 4^{\frac{3}{4}})}^{- 4}$

Step 1

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

$\frac{1}{{(10^{\frac{3}{4}} \cdot 4^{\frac{3}{4}})}^{4}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $10^{\frac{3}{4}} \cdot 4^{\frac{3}{4}}$ .

$\frac{1}{{(10^{\frac{3}{4}})}^{4} \cdot {(4^{\frac{3}{4}})}^{4}}$

Step 2.2

Multiply the exponents in ${(10^{\frac{3}{4}})}^{4}$ .

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Step 2.2.1

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

$\frac{1}{10^{\frac{3}{4} \cdot 4} \cdot {(4^{\frac{3}{4}})}^{4}}$

Step 2.2.2

Cancel the common factor of $4$ .

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Step 2.2.2.1

Cancel the common factor.

$\frac{1}{10^{\frac{3}{4} \cdot 4} \cdot {(4^{\frac{3}{4}})}^{4}}$

Step 2.2.2.2

Rewrite the expression.

$\frac{1}{10^{3} \cdot {(4^{\frac{3}{4}})}^{4}}$

Step 2.3

Raise $10$ to the power of $3$ .

$\frac{1}{1000 \cdot {(4^{\frac{3}{4}})}^{4}}$

Step 2.4

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

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Step 2.4.1

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

$\frac{1}{1000 \cdot 4^{\frac{3}{4} \cdot 4}}$

Step 2.4.2

Cancel the common factor of $4$ .

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Step 2.4.2.1

Cancel the common factor.

$\frac{1}{1000 \cdot 4^{\frac{3}{4} \cdot 4}}$

Step 2.4.2.2

Rewrite the expression.

$\frac{1}{1000 \cdot 4^{3}}$

Step 2.5

Raise $4$ to the power of $3$ .

$\frac{1}{1000 \cdot 64}$

Step 3

Multiply $1000$ by $64$ .

$\frac{1}{64000}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{64000}$

Decimal Form:

$1.5625 \cdot 10^{- 5}$