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Question
Simplify:
`(27a^9)^((-1)/3) (64a^15)^(2/3)`
Simplify
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Solution
Let’s simplify the expression:
`(27a^9)^(-1/3) * (64a^15)^(2/3)`
Step 1: Apply the power rule: `(x^m)^n = x^(mn)`
`(27a^9)^(-1/3) = 27^(-1/3) * a^(9*(-1/3))`
= `3^(-3 * 1/3) * a^-3`
= `3^-1 * a^-3`
`(64a^15)^(2/3) = 64^(2/3) * a^(15 * 2/3)`
= `4^2 * a^10`
= `16a^10`
Step 2: Multiply the simplified parts:
`3^-1 * a^-3 * 16a^10`
= `1/3 * 16 * a^(-3 + 10)`
= `16/3 a^7`
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Chapter 6: Indices - MISCELLANEOUS EXERCISE [Page 69]
