Question

What is the value of the expression if m = –5 and n = 3? Negative StartFraction 24 Over 25 EndFraction Negative StartFraction 4 Over 25 EndFraction StartFraction 4 Over 25 EndFraction StartFraction 24 Over 25 EndFraction.

Answer 1

You can use the fact that  a number raised to negative powers can be written as 1 divided by that number raised to positive number.

The value of the given expression when m = -5 and n= 3 is $-\dfrac{2}{5}$

How can we rewrite a number raised to negative power?

Suppose we've got $a^{-b}$ . then it can be rewritten as

$a^{-b} = \dfrac{1}{a^b}$

It is because $a^0 = 1$ for any a except 0, and that  $\dfrac{a^0}{a^b} = a^{0-b} = a^{-b}$

If base are same and there is multiplication, then there will be addition in power.

Also, know the fact that if base are same and there is division, there will be subtraction in power(subtracting since that denominator when goes up, its power gets negated(gets negative sign to the existing power)

Thus,

$a^b \timesa ^c = a^{b+c}\\\\\dfrac{a^b}{a^c} = a^{b-c}$

Using above method to simplify the given expression before evaluating

The given expression is $\dfrac{2m^{-1}n^5}{3m^0n^4} = \dfrac{2n^5}{3m^0m^1n^4} = \dfrac{2n^5}{3mn^4} = \dfrac{2n^{5-4}}{3m} = \dfrac{2n^1}{3m} = \dfrac{2n}{3m}$

Putting m = -5 and n=3, we get:

$\dfrac{2\times 3}{3 \times -5} = -\dfrac{2}{5}$

Thus,

The value of the given expression when m = -5 and n= 3 is $-\dfrac{2}{5}$

Learn more about base and exponent(power) here:

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