Question

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If 2160 = 2m × 3n × 5p, find the value of m, n and p. Hence evaluate $(-1)^m × 2^n × 10^p$​

Answer 1

Step-by-step explanation:

2m × 3n × 5p = 30mnp =2160

therefore,

mnp = 2160/30

mnp = 72

factors of 72 = 2 × 2 × 2 × 3 ×3

72 = 2 × (2×2) × (3×3)

we can write,

mnp = 2 × (2×2) × (3×3)

You can try these values,

m = 2

n = 2×2 = 4

p = 3×3 = 9

Answer 2

The correct Question is -

$\dashrightarrow\:\:\sf 2160 = {2}^m \times 3^{n} \times 5^{p}$

We have to find the value of m, n and p.

Also , evaluate $(-1)^m × 2^n × 10^p$

What we have to do ?

Here, we are going to use the concept of prime factorization Method. Prime factorization is a method which basically used to find out the one and only factors (prime factors) of the particular number. There after we will compare the values and then we will have our answer.

$\bigstar\:\underline{\textbf{Let's solve it now :}}$

It is said that in question -

$\dashrightarrow\:\:\sf 2160 = {2}^m \times {3}^n \times {5}^p$

So ,by using prime factorization Method , the factors of 2160 are :

$\sf \longrightarrow 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 5$

Therefore,

$\sf \longrightarrow 2^{4} \times 3^{3} \times 5^{1}$

Hence, By comparing it with the given expression :-

$\sf \longrightarrow 2160 = 2^{m} \times 3^{n} \times 5^{p}$

We get ,

• $\dashrightarrow\:\:\sf m = 4$
• $\dashrightarrow\:\:\sf n = 3$
• $\dashrightarrow\:\:\sf p = 1$

Now, Substituting the values of m, n and p respectively to find the value of -

$\implies \sf (-1)^{m} × 2^{n} × 10^{p}$

$:\implies \sf (-1)^{4} \times 2^{3} \times 10^{1}$

$:\implies \sf 1 \times 8 \times 10$

$:\implies\boxed{\bf{80}}$

$\dashrightarrow\:\: \underline{ \boxed{\sf Answer = 80}}$

Not sure about the answer ?

Let's Verify it.

Putting up -

$:\implies \sf m = 4$

$:\implies \sf n = 3$

$:\implies \sf p = 1$

In first expression respectively.

$\dashrightarrow\:\:\sf 2160 = 2^{m} \times 3^{n} \times 5^{p}$

$\dashrightarrow\:\:\sf 2160 = 2^{4} \times 3^{3} \times 5^{1}$

$\dashrightarrow\:\:\sf 2160 = 16 \times 27 \times 5$

$\dashrightarrow\:\:\sf 2160 = 2160$

$:\implies \bf LHS = RHS$

$\underline{\sf Verified ! }$