What is [(b^8*(a^3)^4)/(2*b^4*a^6)]^3 ?

The solution to [(b^8*(a^3)^4)/(2*b^4*a^6)]^3 is (b^{12}a^{18})/8

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simplify [(b^8(a^3)^4)/(2b^4*a^6)]^3

simplify

[\frac{b ^{8} \cdot ( a ^{3} ) ^{4}}{2 \cdot b ^{4} \cdot a ^{6}}]^{3}

\frac{b ^{12} a ^{18}}{8}

Solution steps

(\frac{b ^{8} ( a ^{3} ) ^{4}}{2 b ^{4} a ^{6}})^{3}

Apply exponent rule:

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

= \frac{( b ^{8} ( a ^{3} ) ^{4} ) ^{3}}{( 2 b ^{4} a ^{6} ) ^{3}}

Simplify

(b^{8} (a^{3})^{4})^{3} : b^{24} a^{36}

= \frac{b ^{24} a ^{36}}{( 2 b ^{4} a ^{6} ) ^{3}}

Simplify

(2 b^{4} a^{6})^{3} : 8 b^{12} a^{18}

= \frac{b ^{24} a ^{36}}{8 b ^{12} a ^{18}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{b ^{24}}{b ^{12}} = b^{24 - 12}

= \frac{a ^{36} b ^{24 - 12}}{8 a ^{18}}

Subtract the numbers:

24 - 12 = 12

= \frac{b ^{12} a ^{36}}{8 a ^{18}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{a ^{36}}{a ^{18}} = a^{36 - 18}

= \frac{b ^{12} a ^{36 - 18}}{8}

Subtract the numbers:

36 - 18 = 18

= \frac{b ^{12} a ^{18}}{8}

5 + 75

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

- 12 \cdot (- 12)

\frac{( 1.24 \cdot 1 0 ^{2} ) ( 3.6 \cdot 1 0 ^{- 3} )}{1.8 \cdot 10}

cos^{2} (x) + 2 sin^{2} (x)

What is [(b^8*(a^3)^4)/(2*b^4*a^6)]^3 ?
The solution to [(b^8*(a^3)^4)/(2*b^4*a^6)]^3 is (b^{12}a^{18})/8