What is ((5a^2)^3*(6b)^2)/((30a^3b)^2) ?

The solution to ((5a^2)^3*(6b)^2)/((30a^3b)^2) is 5

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simplify ((5a^2)^3*(6b)^2)/((30a^3b)^2)

simplify

\frac{( 5 a ^{2} ) ^{3} \cdot ( 6 b ) ^{2}}{( 30 a ^{3} b ) ^{2}}

5

Solution steps

\frac{( 5 a ^{2} ) ^{3} ( 6 b ) ^{2}}{( 30 a ^{3} b ) ^{2}}

Simplify

(5 a^{2})^{3} : 5^{3} a^{6}

= \frac{5 ^{3} a ^{6} ( 6 b ) ^{2}}{( 30 a ^{3} b ) ^{2}}

Simplify

(30 a^{3} b)^{2} : 3 0^{2} a^{6} b^{2}

= \frac{5 ^{3} a ^{6} ( 6 b ) ^{2}}{3 0 ^{2} a ^{6} b ^{2}}

Factor

3 0^{2} : 5^{2} \cdot 6^{2}

= \frac{5 ^{3} a ^{6} ( 6 b ) ^{2}}{5 ^{2} \cdot 6 ^{2} a ^{6} b ^{2}}

\frac{5 ^{3}}{5 ^{2}} = 5

= \frac{5 a ^{6} ( 6 b ) ^{2}}{6 ^{2} a ^{6} b ^{2}}

Cancel the common factor:

a^{6}

= \frac{5 ( 6 b ) ^{2}}{6 ^{2} b ^{2}}

Apply exponent rule:

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

(6 b)^{2} = 6^{2} b^{2}

= \frac{5 \cdot 6 ^{2} b ^{2}}{6 ^{2} b ^{2}}

Cancel the common factor:

6^{2}

= \frac{5 b ^{2}}{b ^{2}}

Cancel the common factor:

b^{2}

= 5

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(2 a + 2)^{3}

(\frac{2}{3 x - 2 y})^{3}

9 y^{2} (10 y + 2 y^{3})

lo g_{10} (x - 1) - lo g_{10} (x + 2)

What is ((5a^2)^3*(6b)^2)/((30a^3b)^2) ?
The solution to ((5a^2)^3*(6b)^2)/((30a^3b)^2) is 5