Question

Simplify and give reasons
(i)4^-3
(ii) (-2)^7
(iii) (3/4)^-3
(iv) (-3)^-4​

Answer 1

Answer:

$\huge\mathfrak\purple{Solution}$

${4}^{ - 3}$

Using this exponent law:-

${a}^{ - m} = \frac{1}{a^{m} }$

We reciprocal this.

${4}^{ - 3} = \frac{1}{4^{ 3} }$

$\: \: \: \: \: \: \: \: \: = \frac{1}{4 \times 4 \times 4}$

$\: \: \: \: \: \: \: \: \: = \frac{1}{64}$

In 2 part multiply (-2) seven times because it has power of 7

$= {( - 2)}^{7}$

$= ( - 2) \times ( - 2) \times ( - 2) \times ( - 2) \times ( - 2) \times ( - 2) \times ( - 2)$

$= ( - 128)$

To solve this question apply this rule:-

$( \frac{a }{b})^{m} = \frac{a^{m} }{b^{m} }$

$= \frac{3^{ - 3} }{4^{ - 3} }$

$= \frac{4 \times 4 \times 4}{3 \times 3 \times 3 }$

$= \frac{64}{27}$

In fourth part same rule apply as first.

$= {( - 3)}^{( - 4)}$

$= \frac{1}{( - 3) \times ( - 3) \times ( - 3) \times ( - 3)}$

$= \frac{1}{81}$

Step-by-step explanation:

Hope this helps you.

# By Sparkly Princess