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How do you simplify ${m^4}.2{m^{ - 3}}$ and write it using only positive exponents?

Last updated date: 23rd Jul 2024
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Hint: In this question, we are given two exponents having the same base “m” in multiplication with each other and we have to simplify this expression, that is, we have to write it easily and understandably. So , we can solve the question by using the law which states that when two numbers having the same base but different powers are multiplied then keeping the base same, we add the powers, that is, ${x^a} \times {x^b} = {x^{a + b}}$.

Complete step-by-step solution:
We are given that ${m^4}.2{m^{ - 3}}$
Keeping the base same, we add the powers –
  {m^4}2{m^{ - 3}} = 2{m^{4 - 3}} \\
   \Rightarrow {m^4}2{m^{ - 3}} = 2m \\
The power of m is equal to 1 and it is a positive number.
Hence the simplified form of ${m^4}2{m^{ - 3}}$ is $n$ .

Note: We know that when the exponent is negative then we write the number as the reciprocal of the given exponent to convert it into a positive exponent, that is, ${a^{ - x}} = \dfrac{1}{{{a^x}}}$ . So, $2{m^{ - 3}}$ can be written as $\dfrac{2}{{{m^3}}}$ . Now, the given expression becomes $\dfrac{{2{m^4}}}{{{m^3}}}$ . Thus, the expression obtained is a fraction and we know that for simplifying a fraction we write the numerator and the denominator as a product of its prime factors

After doing the prime factorization of the numerator and the denominator, we cancel out the common factors until there are no common factors present between the numerator and the denominator.
${m^4}$ can be written as $m \times m \times m \times m$
And ${m^3}$ can be written as \[m \times m \times m\]
Thus we see that the numerator and the denominator have $m \times m \times m$ or ${m^3}$ as common, so it is canceled out and we get –
$\dfrac{{2{m^4}}}{{{m^3}}} = 2m$