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प्रश्न
Simplify:
`((9)^3 xx 27 xx t^4)/((3)^-2 xx (3)^4 xx t^2)`
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उत्तर
Given, `((9)^3 xx 27 xx t^4)/((3)^-2 xx (3)^4 xx t^2)`
= `((3^2)^3 xx (3)^3 xx t^4)/((3)^-2 xx (3)^4 xx t^2)` ...[∵ 3 × 3 = 32 = 9]
= `((3)^6 xx (3)^3 xx t^4)/((3)^-2 xx (3)^4 xx t^2)`
= (3)6 × (3)3 × (3)2 × (3)–4 × t4 × t–2 ...`[∵ a^-m = 1/a^m]`
= (3)11 – 4 × t4 – 2 ...[∵ am × an = (a)m – n]
= (3)7 × t2
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संबंधित प्रश्न
The value of `(2/5)^-2` is ______.
If x be any non-zero integer, then x–1 is equal to ______.
`(1/10)^0` is equal to ______.
The value of [2–1 × 3–1]–1 is ______.
The expression for 35 with a negative exponent is ______.
329.25 = 3 × 102 + 2 × 101 + 9 × 100 + 2 × 10–1 + 5 × 10–2
An insect is on the 0 point of a number line, hopping towards 1. She covers half the distance from her current location to 1 with each hop. So, she will be at `1/2` after one hop, `3/4` after two hops, and so on.
- Make a table showing the insect’s location for the first 10 hops.
- Where will the insect be after n hops?
- Will the insect ever get to 1? Explain.
If possible, find a hook-up of prime base number machine that will do the same work as the given stretching machine. Do not use (× 1) machines.
Find x.
`(2/5)^(2x + 6) xx (2/5)^3 = (2/5)^(x + 2)`
Simplify:
`(1/5)^45 xx (1/5)^-60 - (1/5)^(+28) xx (1/5)^-43`
