Question

Solve this problem

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Answer 1

Step-by-step explanation:

Given:

$a) {a}^{m} + {a}^{n} = {a}^{m + n} \\ \\ b) {(1024)}^{ \frac{ - 1}{5} } = \frac{1}{4} \\ \\ c)( { - 1)}^{101} + {( - 1)}^{50} = 0 \\ \\ d) {(0.0027)}^{ \frac{1}{3} } = 0.3$

To find: Which statement is correct

Solution:

Option C is correct.

Hint:

$( - a) ^{n} = - a \: \: \: if \: n \: is \: odd \\ \\ ( - a) ^{n} = a \: \: \: if \: n \: is \:even$

Thus,

$( { - 1)}^{101} = - 1 \\ \\ ( { - 1)}^{50} = 1 \\ \\ - 1 + 1 = 0$

By this way, option C is correct.

Hope it helps you.

Answer 2

Given:

• $\sf a^m + a^n = a^{m+n} , where \ a \neq 0$
• $\sf (1024)^{- \dfrac {1}{5}} = \dfrac {1}{4}$
• $\sf (-1)^{101} + (-1)^{50} = 0$
• $\sf (0.0027)^{\dfrac {1}{3}}$

To find:

• Which is the correct statement.

Solution:

We know that,

$\leadsto \sf (-a)^n = -a \ if \ n \ is \ odd$

$\leadsto \sf (-a)^n = a \ if \ n \ is \ even$

$\sf Therefore,$

$\leadsto \sf (-1)^{101} \ = \ -1$

$\leadsto \sf (-1)^{50} \ = \ 1$

$\leadsto \sf -1 + 1 = 0$

$\bf Therefore, \ option \ C \ is \ correct.$