Basic Math Examples

${(- 243^{\frac{3}{10}})}^{2}$

Step 1

Simplify the expression.

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Step 1.1

Apply the product rule to $- 243^{\frac{3}{10}}$ .

${(- 1)}^{2} {(243^{\frac{3}{10}})}^{2}$

Step 1.2

Raise $- 1$ to the power of $2$ .

$1 {(243^{\frac{3}{10}})}^{2}$

Step 1.3

Multiply ${(243^{\frac{3}{10}})}^{2}$ by $1$ .

${(243^{\frac{3}{10}})}^{2}$

Step 1.4

Multiply the exponents in ${(243^{\frac{3}{10}})}^{2}$ .

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Step 1.4.1

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

$243^{\frac{3}{10} \cdot 2}$

Step 1.4.2

Cancel the common factor of $2$ .

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Step 1.4.2.1

Factor $2$ out of $10$ .

$243^{\frac{3}{2 (5)} \cdot 2}$

Step 1.4.2.2

Cancel the common factor.

$243^{\frac{3}{2 \cdot 5} \cdot 2}$

Step 1.4.2.3

Rewrite the expression.

$243^{\frac{3}{5}}$

Step 1.5

Rewrite $243$ as $3^{5}$ .

${(3^{5})}^{\frac{3}{5}}$

Step 1.6

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

$3^{5 (\frac{3}{5})}$

Step 2

Cancel the common factor of $5$ .

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Step 2.1

Cancel the common factor.

$3^{5 (\frac{3}{5})}$

Step 2.2

Rewrite the expression.

$3^{3}$

Step 3

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

$27$