Question

CLASS 7 MATHS

CH-13- EXPONENTS AND POWERS

FIND THE RECIPROCAL OF

A) $(-2/3)^{4}$

B) $(-2/3)^{3}$ × $(3/4)^{4}$

Answer 1

A.) Find the reciprocal of ( -2/3 )⁴ .

$\begin{lgathered}\sf = { (\frac{ - 2}{3}) }^{4} . \\ \\ \sf = \frac{ - 2 \times - 2 \times - 2 \times - 2}{3 \times 3 \times 3 \times 3 } . \\ \\ \sf = \frac{16}{81} . \\ \\ \sf the \: reciprocal \: is \: \large \boxed{ \pink{ = \frac{81}{16} .}}\end{lgathered}$

B.) Find the reciprocal of ( -2/3 )³ × ( 3/4 )⁴ .

$\begin{lgathered}\sf = {( \frac{ - 2}{3} )}^{3} \times { (\frac{3}{4} )}^{4} . \\ \\ \sf = \frac{ - 2 \times - 2 \times - 2 \times \cancel3 \times \cancel3 \times \cancel3 \times 3}{ \cancel3 \times \cancel3 \times \cancel3 \times 4 \times 4 \times 4 \times 4} . \\ \\ \sf = \frac{ - 2 \times - 2 \times - 2 \times 3 }{4 \times 4 \times 4 \times 4} . \\ \\ \sf = \frac{ - 3}{2 \times 2 \times 2 \times 4} . \\ \\ \sf = \frac{ - 3}{32} . \\ \\ \sf the \: reciprocal \: is \: \huge \boxed{ \pink{ \sf = \frac{ - 32}{3} .}}\end{lgathered}$

✔✔ Hence, it is solved ✅✅.