Algebra Examples

$\sqrt[3]{8^{x}} = 65536$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{8^{x}}$ as $8^{\frac{x}{3}}$ .

$8^{\frac{x}{3}} = 65536$

Step 2

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

$2^{3 \frac{x}{3}} = 2^{16}$

Step 3

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

$3 \frac{x}{3} = 16$

Step 4

Cancel the common factor of $3$ .

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Step 4.1

Cancel the common factor.

$3 \frac{x}{3} = 16$

Step 4.2

Rewrite the expression.

$x = 16$