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प्रश्न
Use the properties of exponents to verify that statement is true.
`4^(n - 1) = 1/4(4)^n`
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उत्तर
LHS = 4n – 1
= 4n ÷ 41 ...[∵ am ÷ an = (a)m – n]
= `4^n/4`
= RHS
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संबंधित प्रश्न
For a non-zero integer x, x7 ÷ x12 is equal to ______.
The value of (7–1 – 8–1) –1 – (3–1 – 4–1) –1 is ______.
By multiplying `(5/3)^4` by ______ we get 54.
50 = 5
Express as a power of a rational number with negative exponent.
`(((-3)/2)^-2)^-3`
Simplify:
`(49 xx z^-3)/(7^-3 xx 10 xx z^-5) (z ≠ 0)`
By what number should we multiply (–29)0 so that the product becomes (+29)0.
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.
Will the insect ever get to 1? Explain.
The left column of the chart lists the lengths of input chains of gold. Repeater machines are listed across the top. The other entries are the outputs you get when you send the input chain from that row through the repeater machine from that column. Copy and complete the chart.
| Input Length | Repeater Machine | ||
| × 23 | |||
| 40 | 125 | ||
| 2 | |||
| 162 | |||
Simplify:
`((3^-2)^2 xx (5^2)^-3 xx (t^-3)^2)/((3^-2)^5 xx (5^3)^-2 xx (t^-4)^3`
