Basic Math Examples

${(0.2)}^{\frac{2}{3}} {(0.2)}^{\frac{4}{3}} {(0.2)}^{\frac{7}{6}}$

Step 1

Multiply ${(0.2)}^{\frac{2}{3}}$ by ${(0.2)}^{\frac{4}{3}}$ by adding the exponents.

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Step 1.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${0.2}^{\frac{2}{3} + \frac{4}{3}} {(0.2)}^{\frac{7}{6}}$

Step 1.2

Combine the numerators over the common denominator.

${0.2}^{\frac{2 + 4}{3}} {(0.2)}^{\frac{7}{6}}$

Step 1.3

Add $2$ and $4$ .

${0.2}^{\frac{6}{3}} {(0.2)}^{\frac{7}{6}}$

Step 1.4

Divide $6$ by $3$ .

${0.2}^{2} {(0.2)}^{\frac{7}{6}}$

Step 2

Multiply ${0.2}^{2}$ by ${(0.2)}^{\frac{7}{6}}$ by adding the exponents.

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Step 2.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${0.2}^{2 + \frac{7}{6}}$

Step 2.2

To write $2$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

${0.2}^{2 \cdot \frac{6}{6} + \frac{7}{6}}$

Step 2.3

Combine $2$ and $\frac{6}{6}$ .

${0.2}^{\frac{2 \cdot 6}{6} + \frac{7}{6}}$

Step 2.4

Combine the numerators over the common denominator.

${0.2}^{\frac{2 \cdot 6 + 7}{6}}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $2$ by $6$ .

${0.2}^{\frac{12 + 7}{6}}$

Step 2.5.2

Add $12$ and $7$ .

${0.2}^{\frac{19}{6}}$

Step 3

Raise $0.2$ to the power of $\frac{19}{6}$ .

$0.00611779$