Question

Simplify(-4) -¹⁰

*(-4)⁵

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Answer 1

$\huge\underline{\overline{\mid{\bold{\mathfrak{\green{Answer}\mid}}}}}$

$= {( - 4)}^{ - 10} \times {( - 4)}^{5} \\ = {( - 4)}^{ - 10 + 5 } \\ {\boxed{= { ( - 4)}^{ - 5} }}$

Answer 2

$\rm \star \bigstar {\underline{ \red Concept }} \bigstar \star$

Here in this query, we have to simplify this by applying, one of the laws of exponent formula which is -

$\small \dagger\rm \boxed{ \rm ({a}^{m} \times {a}^{n}) = \: {a}^{m + n} } \dagger$

$\rm \star \bigstar {\underline{ \red Solution }} \bigstar \star$

We know,

$\small\rm ({a}^{m} \times {a}^{n}) = \: {a}^{m + n}$

$\small \implies\rm {(-4)}^{-10} \times {(-4)}^{5}$

$\small \rm \implies \: {( - 4)}^{-10 + 5}$

$\small \rm \implies \: ( - 4) {}^{ - 5}$

$\rm \star \bigstar {\underline{ \red Laws \: of \: exponent }} \bigstar \star$

Here , are the formulae of laws of exponent:-

• $\small \rm {a}^{m} \times {a}^{n} = {a}^{m + n}$
• $\small \rm \: ( {a}^{m} ) {}^{n} = {a}^{m \times n}$

• $\small \rm \: (ab) {}^{m} = {a}^{m} \times {b}^{m}$

• $\small \rm \: \frac{a {}^{n} }{a {}^{m} } = {a}^{n - m}$

• $\small \rm \: \frac{a {}^{n} }{a {}^{m} } = \frac{1}{ {a}^{m - n} }$

• $\small \rm \: ( \frac{a}{b} ) { }^{n} = ( \frac{ {a}^{n} }{ {b}^{n}} )$

$\\ \bigstar{ \underline{ \underline \pink{ \sf★@iTzShInNy☆}}} \bigstar$