Calculus Examples

$lim_{x \to 1000} x^{\frac{7}{3}}$

Step 1

Move the exponent $\frac{7}{3}$ from $x^{\frac{7}{3}}$ outside the limit using the Limits Power Rule.

${(lim_{x \to 1000} x)}^{\frac{7}{3}}$

Step 2

Evaluate the limit of $x$ by plugging in $1000$ for $x$ .

$1000^{\frac{7}{3}}$

Step 3

Simplify the answer.

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Step 3.1

Rewrite $1000$ as $10^{3}$ .

${(10^{3})}^{\frac{7}{3}}$

Step 3.2

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

$10^{3 (\frac{7}{3})}$

Step 3.3

Cancel the common factor of $3$ .

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Step 3.3.1

Cancel the common factor.

$10^{3 (\frac{7}{3})}$

Step 3.3.2

Rewrite the expression.

$10^{7}$

Step 3.4

Raise $10$ to the power of $7$ .

$10000000$