Basic Math Examples

${(49^{\frac{1}{4}} \cdot 64^{- \frac{1}{4}})}^{2}$

Step 1

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

${(49^{\frac{1}{4}} \cdot \frac{1}{64^{\frac{1}{4}}})}^{2}$

Step 2

Combine fractions.

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Step 2.1

Combine $49^{\frac{1}{4}}$ and $\frac{1}{64^{\frac{1}{4}}}$ .

${(\frac{49^{\frac{1}{4}}}{64^{\frac{1}{4}}})}^{2}$

Step 2.2

Apply the product rule to $\frac{49^{\frac{1}{4}}}{64^{\frac{1}{4}}}$ .

$\frac{{(49^{\frac{1}{4}})}^{2}}{{(64^{\frac{1}{4}})}^{2}}$

Step 3

Simplify the numerator.

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Step 3.1

Multiply the exponents in ${(49^{\frac{1}{4}})}^{2}$ .

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Step 3.1.1

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

$\frac{49^{\frac{1}{4} \cdot 2}}{{(64^{\frac{1}{4}})}^{2}}$

Step 3.1.2

Cancel the common factor of $2$ .

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Step 3.1.2.1

Factor $2$ out of $4$ .

$\frac{49^{\frac{1}{2 (2)} \cdot 2}}{{(64^{\frac{1}{4}})}^{2}}$

Step 3.1.2.2

Cancel the common factor.

$\frac{49^{\frac{1}{2 \cdot 2} \cdot 2}}{{(64^{\frac{1}{4}})}^{2}}$

Step 3.1.2.3

Rewrite the expression.

$\frac{49^{\frac{1}{2}}}{{(64^{\frac{1}{4}})}^{2}}$

Step 3.2

Rewrite $49$ as $7^{2}$ .

$\frac{{(7^{2})}^{\frac{1}{2}}}{{(64^{\frac{1}{4}})}^{2}}$

Step 3.3

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

$\frac{7^{2 (\frac{1}{2})}}{{(64^{\frac{1}{4}})}^{2}}$

Step 3.4

Cancel the common factor of $2$ .

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Step 3.4.1

Cancel the common factor.

$\frac{7^{2 (\frac{1}{2})}}{{(64^{\frac{1}{4}})}^{2}}$

Step 3.4.2

Rewrite the expression.

$\frac{7^{1}}{{(64^{\frac{1}{4}})}^{2}}$

Step 3.5

Evaluate the exponent.

$\frac{7}{{(64^{\frac{1}{4}})}^{2}}$

Step 4

Simplify the denominator.

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Step 4.1

Multiply the exponents in ${(64^{\frac{1}{4}})}^{2}$ .

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Step 4.1.1

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

$\frac{7}{64^{\frac{1}{4} \cdot 2}}$

Step 4.1.2

Cancel the common factor of $2$ .

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Step 4.1.2.1

Factor $2$ out of $4$ .

$\frac{7}{64^{\frac{1}{2 (2)} \cdot 2}}$

Step 4.1.2.2

Cancel the common factor.

$\frac{7}{64^{\frac{1}{2 \cdot 2} \cdot 2}}$

Step 4.1.2.3

Rewrite the expression.

$\frac{7}{64^{\frac{1}{2}}}$

Step 4.2

Rewrite $64$ as $8^{2}$ .

$\frac{7}{{(8^{2})}^{\frac{1}{2}}}$

Step 4.3

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

$\frac{7}{8^{2 (\frac{1}{2})}}$

Step 4.4

Cancel the common factor of $2$ .

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Step 4.4.1

Cancel the common factor.

$\frac{7}{8^{2 (\frac{1}{2})}}$

Step 4.4.2

Rewrite the expression.

$\frac{7}{8^{1}}$

Step 4.5

Evaluate the exponent.

$\frac{7}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{8}$

Decimal Form:

$0.875$