What is (log_{10}(a)log_{10}(c)blog_{10}(a))^3 ?

The solution to (log_{10}(a)log_{10}(c)blog_{10}(a))^3 is b^3log_{10}(a)^6log_{10}(c)^3

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simplify (log_{10}(a)log_{10}(c)blog_{10}(a))^3

simplify

(lo g_{10} (a) lo g_{10} (c) b lo g_{10} (a))^{3}

b^{3} lo g_{10} (a)^{6} lo g_{10} (c)^{3}

Solution steps

(lo g_{10} (a) lo g_{10} (c) b lo g_{10} (a))^{3}

Apply exponent rule:

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

(lo g_{10} (a) lo g_{10} (c) b lo g_{10} (a))^{3} = lo g_{10} (a)^{3} lo g_{10} (c)^{3} b^{3} lo g_{10} (a)^{3}

= lo g_{10} (a)^{3} lo g_{10} (c)^{3} b^{3} lo g_{10} (a)^{3}

Apply exponent rule:

a^{m} b^{m} = (ab)^{m},

assuming

a \geq 0, b \geq 0

b^{3} lo g_{10} (a)^{3} lo g_{10} (a)^{3} lo g_{10} (c)^{3} = (b lo g_{10} (a) lo g_{10} (a) lo g_{10} (c))^{3}

= (b lo g_{10} (a) lo g_{10} (a) lo g_{10} (c))^{3}

Simplify

lo g_{10} (a) lo g_{10} (c) b lo g_{10} (a) : b lo g_{10} (a)^{2} lo g_{10} (c)

= (b lo g_{10} (a)^{2} lo g_{10} (c))^{3}

Apply exponent rule:

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

= b^{3} lo g_{10} (c)^{3} (lo g_{10} (a)^{2})^{3}

(lo g_{10} (a)^{2})^{3} : lo g_{10} (a)^{6}

= b^{3} lo g_{10} (a)^{6} lo g_{10} (c)^{3}

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\frac{7 p ^{6}}{7 c ^{6}}

What is (log_{10}(a)log_{10}(c)blog_{10}(a))^3 ?
The solution to (log_{10}(a)log_{10}(c)blog_{10}(a))^3 is b^3log_{10}(a)^6log_{10}(c)^3