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Question
`[(2/13)^-6 ÷ (2/13)^3]^3 xx (2/13)^-9` = ______.
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Solution
`[(2/13)^-6 ÷ (2/13)^3]^3 xx (2/13)^-9` = `underlinebb((2/13)^-36)`.
Explanation:
Using laws of exponents,
am ÷ an = (a)m – n and am × an = (a)m + n ...[∵ a is non-zero integer]
∴ `[(2/13)^-6 ÷ (2/13)^3]^3 xx (2/13)^-9 = [(2/13)^(-6 - 3)]^3 xx (2/13)^-9`
= `(2/13)^-27 xx (2/13)^-9`
= `(2/13)^(-27 - 9)`
= `(2/13)^-36`
Hence, `[(2/13)^-6 ÷ (2/13)^3]^3 xx (2/13)^-9 = (2/13)^-36`
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