Question

$\small \red{ \underline{ \underline{question}}}$
1. by what number should (-5)-1 be multiplied so that the product 8s (8)-1?
2. Find x such that (3/5)pwer3 ×(3/5)powr2x-1 ​

Answer 1

Answer :

1. Let us consider the number as x

According to the question :

$\tt{ {(-5)}^{-1} \times x \implies {(8)}^{-1}}$

$\tt{ After \: taking\: the \:numbers\: in\: fraction \: we \: get :}$

$\tt{ \dfrac{1}{-5} \times x \implies \dfrac{1}{8}}$

It is necessary to convert the integers into fraction form to make the powers positive.

Then we will transpose the terms :

$\tt{ x \implies \dfrac{1}{-5} \div \dfrac{1}{8}}$

$\tt{ x \implies \dfrac{1}{-5} \times \dfrac{8}{1}}$

$\tt{ x \implies \dfrac{-5}{8}}$

So the number by which when multiplied gives (8)^(-1) is

$\boxed{\tt{ \dfrac{-5}{8}}}$

2.

$\tt{ {\dfrac{3}{5}}^{3} \times {\dfrac{3}{5}}^{-6} \implies {\dfrac{3}{5}}^{2x+1}}$

As the bases are same ; we will just calculate the powers directly.

The following is the calculation of powers :

$\tt{ 3 + (-6) = 2x - 1}$

$\tt{ -3 = 2x -1}$

Transposing -3 gives :

$\tt{ 2x = -3 + 1 }$

$\tt{ x = \dfrac{2x}{-2}}$

$\tt{ x = \dfrac{2}{-2}}$

$\tt{ x = (-1)}$

Answer 2

Answer:

1 painting today is ew for me

2 it totally depends on the person