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Popular >

simplify (3a^3b^{-1}a)^2

Solution

simplify

(3 a^{3} b^{- 1} a)^{2}

Solution

\frac{9 a ^{8}}{b ^{2}}

Solution steps

(3 a^{3} b^{- 1} a)^{2}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(3 a^{3} b^{- 1} a)^{2} = 3^{2} (a^{3})^{2} (b^{- 1})^{2} a^{2}

= 3^{2} (a^{3})^{2} (b^{- 1})^{2} a^{2}

3^{2} = 9

= 9 (a^{3})^{2} (b^{- 1})^{2} a^{2}

Simplify

(a^{3})^{2} : a^{6}

= 9 a^{6} (b^{- 1})^{2} a^{2}

Simplify

(b^{- 1})^{2} : \frac{1}{b ^{2}}

= 9 a^{6} \frac{1}{b ^{2}} a^{2}

Apply exponent rule:

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

a^{6} a^{2} = a^{6 + 2}

= 9 \cdot \frac{1}{b ^{2}} a^{6 + 2}

Add the numbers:

6 + 2 = 8

= 9 \cdot \frac{1}{b ^{2}} a^{8}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 9 a ^{8}}{b ^{2}}

Multiply the numbers:

1 \cdot 9 = 9

= \frac{9 a ^{8}}{b ^{2}}

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Frequently Asked Questions (FAQ)

What is (3a^3b^{-1}a)^2 ?
The solution to (3a^3b^{-1}a)^2 is (9a^8)/(b^2)