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Surds & Indices Questions and Answers

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71.

If \(a^x = b, b^y = c\) and \(c^z = a\), then the value of \(xyz\) is:

Answer: A

Substitute each equation into the next.

\[ c = b^{y} = (a^{x})^{y} = a^{xy} \]

\[ a = c^{z} = (a^{xy})^{z} = a^{xyz} \]

Comparing exponents on the same base:

\[ xyz = 1 \]

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72.

\(125 \times 125 \times 125 \times 125 \times 125 = 5^?\)

Answer: C

\[ 125 = 5^{3} \quad\Longrightarrow\quad 125^{5} = (5^{3})^{5} = 5^{15} \]

So the exponent is 15. Multiplying five copies of \( 5^{3} \) adds their exponents.

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