The denominator of the rational number 275-5000is in the form cube of 2m - 5n- then the value of n is

The number is 2755000 Denominator i.e. 5000 = 2 × 2 × 2 × 5 × 5 × 5 × 5 #160; =2^3× 5^4 = 2^m× 5^n ∴ n = 4 ...

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Standard XII

Mathematics

nth Term of A.P

The denominat...

Question

The denominator of the rational number $\frac{275}{5000}$ is in the form $($ cube of $2^{m} \times 5^{n})$ , then the value of $n$ is

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Solution

The number is $\frac{275}{5000}$
Denominator i.e. $5000 = 2 \times 2 \times 2 \times 5 \times 5 \times 5 \times 5$
$= 2^{3} \times 5^{4}$
$= 2^{m} \times 5^{n}$
$∴ n = 4$

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[NCERT]

Write the denominator of the rational number 257 / 5000 in the form 2 raise to power m into 5 raise to power n where M and n are nonnegative

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The denominator of the rational number 2755000is in the form (cube of 2m×5n), then the value of n is

The number is 2755000Denominator i.e. 5000=2×2×2×5×5×5×5 =23×54=2m×5n∴n=4

The denominator of the rational number $\frac{275}{5000}$ is in the form $($ cube of $2^{m} \times 5^{n})$ , then the value of $n$ is

The number is $\frac{275}{5000}$
Denominator i.e. $5000 = 2 \times 2 \times 2 \times 5 \times 5 \times 5 \times 5$
$= 2^{3} \times 5^{4}$
$= 2^{m} \times 5^{n}$
$∴ n = 4$