By what number should \(5^{-1}\) be multiplied so that the product ma

1.	By what number should \(5^{-1}\) be multiplied so that the product may be equal to \((-7)^{-1}\) ?
Answer» Let the number should \(5^{-1}\) be multiplied by x According to the question: \(x\times 5^{-1}=(-7)^{-1}\) \(x\times \frac{1}{5}=\frac{1}{-7}\)[Using \(a^{-n}=\frac{1}{a^{n}}\)] \(x=\frac{1}{-7}\div \frac{5}{1}=\frac{5}{-7}\) \(x=\frac{1}{-7}\times \frac{5}{1}=\frac{5}{-7}\)= \(-\frac{5}{7}\)[Using and \(\frac{1}{a}\div \frac{1}{b}=\frac{1}{a}\times \frac{b}{1}\)] Therefore \(5^{-1}\) should be multiplied by \(\frac{-5}{7}\)

By what number should \(5^{-1}\) be multiplied so that the product may be equal to \((-7)^{-1}\) ?

Answer»

Let the number should \(5^{-1}\) be multiplied by x

According to the question:

\(x\times 5^{-1}=(-7)^{-1}\)

\(x\times \frac{1}{5}=\frac{1}{-7}\)[Using \(a^{-n}=\frac{1}{a^{n}}\)]

\(x=\frac{1}{-7}\div \frac{5}{1}=\frac{5}{-7}\)

\(x=\frac{1}{-7}\times \frac{5}{1}=\frac{5}{-7}\)= \(-\frac{5}{7}\)[Using and \(\frac{1}{a}\div \frac{1}{b}=\frac{1}{a}\times \frac{b}{1}\)]

Therefore \(5^{-1}\) should be multiplied by \(\frac{-5}{7}\)

Simplify:(i) (4-1 × 3-1)2(ii) (5-1 ÷ 6-1)3(iii) (2-1 + 3-1)-1
Write each of the following in exponential form:(i) \((\frac{3}{2})^{-1}\times (\frac{3}{2})^{-1}\times (\frac{3}{2})^{-1}\times (\frac{3}{2})^{-1}\)(ii) \((\frac{2}{5})^{-2}\times (\frac{2}{5})^{-2}\times (\frac{2}{5})^{-2}\)
By what number should (-15)-1 be divided so that the quotient may be equal to (-5)-1 ?
By what number should \((-15)^{-1}\) be divided so that the quotient may be equal to \((-5)^{-1}\)?
By what number should (1/2)-1 be multiplied so that the product may be equal to (-4/7)-1 ?
Find x, if(i) \((\frac{1}{4})^{-4}\times (\frac{1}{4})^{-8}=(\frac{1}{4})^{-4x}\)(ii) \((\frac{-1}{2})^{-19}\div (\frac{-1}{2})^{8}=(\frac{-1}{2})^{-2x+1}\)(iii) \((\frac{3}{2})^{-3}\times (\frac{3}{2})^{5}=(\frac{3}{2})^{-2x+1}\)(iv) \((\frac{2}{5})^{-3}\times (\frac{2}{5})^{15}=(\frac{2}{5})^{2+3x}\)(v) \((\frac{5}{4})^{-x}\div (\frac{5}{4})^{-4}=(\frac{5}{4})^{5}\)(vi) \((\frac{8}{3})^{2x+1}\times (\frac{8}{3})^{5}=(\frac{8}{3})^{x+2}\)
By what number should \(5^{-1}\) be multiplied so that the product may be equal to \((-7)^{-1}\) ?
By what number should 5-1 be multiplied so that the product may be equal to (-7)-1 ?
Find x, if(i) (1/4)-4 × (1/4)-8 = (1/4)-4x(ii) (-1/2)-19 ÷ (-1/2)8 = (-1/2)-2x+1(iii) (3/2)-3 × (3/2)5 = (3/2)2x+1
By what number should \((\frac{5}{3})^{-2}\) be multiplied so that the product may be \((\frac{7}{3})^{-1}\)?