Question

Q8, 9
MCQ EXPONETS MATHSWIZ
pls help really urgent

Answer 1

Answer:

-2/3 OR -0.667

-5/2 OR -2.5

Step-by-step explanation:

-1/6 * x = 1/9

:. x = -6/9

:. x = -2/3 OR -0.667

$(\frac{3}{5} )^3 * (\frac{3}{5} )^-6 = (\frac{3}{5} )^2^x^-^1\\\\(\frac{3}{5} )^3^-^6 = (\frac{3}{5} )^2^x^-^1\\\\(\frac{3}{5} )^-^6 = (\frac{3}{5} )^2^x^-^1$

as bases are equal

:. -6 = 2x-1

:. 2x = -5

:. x = -5/2 OR -2.5

Answer 2

Explanation :-

Question-8:–

Let,the number be x

So, To multiply (-6)^-1 to obtain a product 9^-1 is

$\dashrightarrow \sf \: ( - 6) {}^{ - 1} \times x = 9 {}^{ - 1}$

By using exponent and laws,

$\: \: \boxed{ \underline \red{ \sf \: a {}^{ - n} = \dfrac{1}{a {}^{n} } }} \bigstar$

$\dashrightarrow \: \sf \: \dfrac{1}{( - 6 ){}^{1} } \times x \: = \dfrac{1}{9 {}^{1} }$

$\dashrightarrow \: \sf \: \dfrac{ - x}{ 6 } \ \: = \dfrac{1}{9 }$

$\dashrightarrow \: \sf \: \dfrac{ - x}{ \not6 \tiny{2} } \ \: = \dfrac{1}{ \not9 \tiny{3} }$

$\dashrightarrow \: \sf \: - 3x = 2$

$\dashrightarrow \: \sf \: x = \dfrac{ - 2}{3}$

So, the value of x is -2/3

___________________________..

Question-9 :–

$\sf \: \bigg ( \dfrac{3}{5} \bigg) {}^{3} \times \bigg( \dfrac{3}{5} \bigg) {}^{ - 6} = \bigg( \dfrac{3}{5} \bigg) {}^{2x -1 }$

As we need to find the value of x,

By using exponent and laws,

$\: \: \boxed{ \underline \red{ \sf \: a {}^{ m} \times a {}^{n} = {a {}^{m + n} } }} \bigstar$

$\sf \: \bigg ( \dfrac{3}{5} \bigg) {}^{3 - 6} = \bigg( \dfrac{3}{5} \bigg) {}^{2x -1 }$

$\sf \: \bigg ( \dfrac{3}{5} \bigg) {}^{ - 3} = \bigg( \dfrac{3}{5} \bigg) {}^{2x -1 }$

Also we know that,

If bases are equal then powers also must be equal

So,

$\implies \sf \: - 3 = 2x - 1$

$\implies \: \sf \: - 3 + 1 \: = 2x$

$\implies \: \sf \: - 2\: = 2x$

$\implies \: \sf \: x = \dfrac{ - 2}{2}$

$\sf \: x = - 1$

So, the value of x is -1