Ifx-2530- -2528 and y-252- -253- find the value of x3- y2-

Using the properties a^m× a^n=a^m+n and a^m÷ a^n=a^m n, ⇒ x=( 25)^30÷( 25)^28=( 25)^30 28=( 25)^2 ⇒ y=( 25)^2× ( 25)^3=( 25)^2+3=( 25)^5 ⇒ x^3=[( 25)^2]^3 ...

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Standard XII

Mathematics

Logarithmic Differentiation

Ifx=-2530÷ -2...

Question

If $x = (- \frac{2}{5})^{30} \div (- \frac{2}{5})^{28} a n d y = (- \frac{2}{5})^{2} \times (- \frac{2}{5})^{3},$ find the value of $(x^{3} \div y)^{2} .$

\frac{25}{4}

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- \frac{2}{5}

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\frac{4}{25}

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\frac{5}{40}

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Solution

The correct option is C $\frac{4}{25}$
Using the properties $a^{m} \times a^{n} = a^{m + n} a n d a^{m} \div a^{n} = a^{m - n},$

$\Rightarrow x = (- \frac{2}{5})^{30} \div (- \frac{2}{5})^{28} = (- \frac{2}{5})^{30 - 28} = (- \frac{2}{5})^{2}$

$\Rightarrow y = (- \frac{2}{5})^{2} \times (- \frac{2}{5})^{3} = (- \frac{2}{5})^{2 + 3} = (- \frac{2}{5})^{5}$

$\Rightarrow x^{3} = {[(- \frac{2}{5})^{2}]}^{3} = (- \frac{2}{5})^{2 \times 3} = (- \frac{2}{5})^{6} [U s i n g (a^{m})^{n} = a^{m n}]$

$\Rightarrow x^{3} \div y = (- \frac{2}{5})^{6} \div (- \frac{2}{5})^{5} = (- \frac{2}{5})^{6 - 5} = - \frac{2}{5}$

$\Rightarrow (x^{3} \div y)^{2} = (- \frac{2}{5})^{2} = \frac{(- 2)^{2}}{5^{2}} = \frac{4}{25}$

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Ifx=(−25)30÷(−25)28 and y=(−25)2×(−25)3, find the value of (x3÷y)2.

If $x = (- \frac{2}{5})^{30} \div (- \frac{2}{5})^{28} a n d y = (- \frac{2}{5})^{2} \times (- \frac{2}{5})^{3},$ find the value of $(x^{3} \div y)^{2} .$