Monica Capoor Solutions for Chapter: Exponents and Powers, Exercise 4: EXERCISE

Find the simplest form of ${\left(89\right)}^0\times {\left(\frac{9}{4}\right)}^{-2}\times {\left(\frac{2}{3}\right)}^{-3}$.

Simplify the following. $\frac{27\times a^{-4}}{12\times 4^{-3} \times a^{-5}}$

Find the value of $x$ for which $7^{10} ÷ 7^8 ={\left(\frac{1}{7}\right)}^x$

Find the value of $x$ for which ${\left(\frac{2}{5}\right)}^4 \times {\left(\frac{2}{5}\right)}^{-7} ={\left(\frac{2}{5}\right)}^{2x+1}$.

Find the value of $x$ for which ${\left(\frac{-3}{4}\right)}^4 ÷ {\left(\frac{-3}{4}\right)}^3 ={\left(\frac{-4}{3}\right)}^x$

Find the value of $\frac{a}{b}$ for which ${\left(\frac{2}{5}\right)}^{-5} \times {\left(\frac{15}{7}\right)}^{-5} ={\left(\frac{a}{b}\right)}^{-5}$.

By what number should ${\left(-5\right)}^{-1}$ be multiplied so that the product becomes ${\left(-15\right)}^{-1}$?

By what number should ${\left(\frac{-4}{7}\right)}^{-1}$ be divided so that the quotient may be ${\left(\frac{-8}{7}\right)}^{-1}$?