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Popular >

simplify ((1/3)^2)^3*(1/3)^2

Solution

simplify

((\frac{1}{3})^{2})^{3} \cdot (\frac{1}{3})^{2}

Solution

\frac{1}{6561}

+1

Decimal Notation

0.00015 \dots

Solution steps

((\frac{1}{3})^{2})^{3} (\frac{1}{3})^{2}

((\frac{1}{3})^{2})^{3} = \frac{1}{729}

= \frac{1}{729} (\frac{1}{3})^{2}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

(\frac{1}{3})^{2} = \frac{1 ^{2}}{3 ^{2}}

= \frac{1}{729} \cdot \frac{1 ^{2}}{3 ^{2}}

1^{2} = 1

= \frac{1}{729} \cdot \frac{1}{3 ^{2}}

3^{2} = 9

= \frac{1}{729} \cdot \frac{1}{9}

Factor the number:

\frac{1}{729} = (\frac{1}{9})^{3}

= (\frac{1}{9})^{3} \frac{1}{9}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

(\frac{1}{9})^{3} \frac{1}{9} = (\frac{1}{9})^{3 + 1}

= (\frac{1}{9})^{3 + 1}

Add the numbers:

3 + 1 = 4

= (\frac{1}{9})^{4}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{1 ^{4}}{9 ^{4}}

1^{4} = 1

= \frac{1}{9 ^{4}}

9^{4} = 6561

= \frac{1}{6561}

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Frequently Asked Questions (FAQ)

What is ((1/3)^2)^3*(1/3)^2 ?
The solution to ((1/3)^2)^3*(1/3)^2 is 1/6561