Let'sLet's work through the tasks in go the image.

Task 1: Find the values of the expressions

throughFor the the first expressions part: 1 in. $a the) \quad 3^3$ image -:

Solution1: $.3^3 = ** Expression3 \1times 3 \times 3 =**: Find the value27 of$ (
3^24. + ( b3) \quad 12 : 12 ^) 3\ ).

• • Calculate Solution each term separately: : - \( 312^ :4 =12 =81 1 \ )

- Task ( 3^32 =: Simpl27ify\ the)

expressions

For - the Add them together second part: : 1 . - ( ( a3)^ \4quad + \ left3(^ a3 =^{-3 81} + \27 =right )^4 \108cd\ot)

a ^{22} ) So, - the Solution result: of the \ first[ part is \ left108( a.

^{-23.} ** \Expressionright 2**: Simplify a) \left(a^{-3}^right4)^ = a^{-12}4 \ \quadcd \ottext a{^{and22 thus},).

} \ -quad Use a the^{- power12 rule} \ ((cdaot^ am^{)^22n} = = a a^{^{m22 \ -cd ot12 n}}\ =): a ^{ -10 } (\ left ]

• Answer: $a^{10}$

2. b)(a \quad 0.4x^6^{- y3^{-}\8right})^ \4cd = a^{-3 \cdot 4} = a^{-12}
   • Combine powersot: (50ax^{-^{-125}} \ ycd^ot9 a ^{) 22 } - = Solution a: ^{- 12 \ +[ 22 }0 =.4 \ acd^{10ot})

50 = 20 The simplified form for, this \quad expression is x ^6$\acd^{10ot x}$^{-5.

}3 = x. ^{Expression6 3 - :5} = Simpl x,ify \quad y (b) 0.4^{-x8^}6 \ ycd^{-ot8 y^}9 = \ ycd^{ot9 -50 x^{-5} y^98} =\ y ).

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• • Simpl Finalify answer the: constants ( first20:
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4Would \ you like further details on anycdot 50 = part20\ of these) solutions , or do - you have For ( specific questionsx?

###)- Relatedterms: Questions

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ofWould operations play in you simplification?

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^{1m. \cd Howot n}) and product would the solution change if rule we ( werea given different exponents? ^2m \cdot a^n. What rules = apply a when simplifying^{m expressions+n with negative}) exponents can? simplify3 complex. expressions How significantly. would we simplify expressions with fractional exponents? 4. Can we apply these exponent rules to variables with different bases? 5. How does the distributive property differ from the rules for simplifying exponents?

Tip: When multiplying terms with the same base, remember to add the exponents.