DAV Class 7 Maths Chapter 4 Worksheet 2

Exponents and Powers Worksheet 2

1. Find the reciprocals of each of the following

(i) \( (12)^5 \)

Solution:

\begin{align*} \text{Reciprocal } & = \color{red} \left(\frac{1}{12}\right)^5 \\ \\ \end{align*}

(ii) \( (-9)^4 \)

Solution:

\begin{align*} \text{Reciprocal } & = \color{red} \left(-\frac{1}{9}\right)^4 \\ \\ \end{align*}

(iii) \( \displaystyle \left(\frac{2}{7}\right)^3 \)

Solution:

\begin{align*} \text{Reciprocal } & = \color{red} \left(\frac{7}{2}\right)^3 \\ \\ \end{align*}

(iv) \( \displaystyle \left(-\frac{3}{7}\right)^7 \)

Solution:

\begin{align*} \text{Reciprocal } & = \color{red} \left(-\frac{7}{3}\right)^7 \\ \\ \end{align*}

(v) \( \displaystyle \left(-\frac{1}{15}\right)^8 \)

Solution:

\begin{align*} \text{Reciprocal } & = \color{red} \left(-15\right)^8 \\ \\ \end{align*}

(vi) \( \displaystyle \left(-\frac{8}{13}\right)^{99} \)

Solution:

\begin{align*} \text{Reciprocal } & = \color{red} \left(-\frac{13}{8}\right)^{99} \\ \\ \end{align*}

(vii) \( \displaystyle \left(\frac{1}{10}\right)^{10} \)

Solution:

\begin{align*} \text{Reciprocal } & = \color{red} \left(10\right)^{10} \\ \\ \end{align*}

(viii) \( \displaystyle \frac{2}{3} \times \frac{9}{4} \)

Solution:

\begin{align*} & = \frac{\cancel2^1}{\cancel3_1} \times \frac{\cancel9^3}{\cancel4_2} \\ \\ & = \frac{3}{2} \\ \\ \text{Reciprocal } & = \color{red} \frac{2}{3} \\ \\ \end{align*}

(ix) \( \displaystyle \left(\frac{1}{2}\right)^2 \times 4 \)

Solution:

\begin{align*} & = \left(\frac{1}{2}\right)^2 \times 4 \\ \\ & = \frac{1}{2} \times \frac{1}{2} \times 4 \\ \\ & = \frac{1}{\cancel4_1} \times \cancel4_1 \\ \\ & = 1 \\ \\ \text{Reciprocal } & = \color{red} 1 \\ \\ \end{align*}

(x) \( \displaystyle -\left(\frac{7}{8}\right)^2 \)

Solution:

\begin{align*} \text{Reciprocal } & = \color{red} -\left(\frac{8}{7}\right)^2 \\ \\ \end{align*}