Basic Math Examples

$49^{16^{- 4^{- 1}}}$

Step 1

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

$49^{16^{- \frac{1}{4}}}$

Step 2

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

$49^{\frac{1}{16^{\frac{1}{4}}}}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite $16$ as $2^{4}$ .

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

Step 3.2

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

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

Step 3.3

Cancel the common factor of $4$ .

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Step 3.3.1

Cancel the common factor.

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

Step 3.3.2

Rewrite the expression.

$49^{\frac{1}{2^{1}}}$

Step 3.4

Evaluate the exponent.

$49^{\frac{1}{2}}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

Cancel the common factor of $2$ .

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Step 4.3.1

Cancel the common factor.

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

Step 4.3.2

Rewrite the expression.

$7^{1}$

Step 5

Evaluate the exponent.

$7$