1.

[tex]5^{3} x^{5*3} = 125x^{15}[/tex]

2.

[tex]10^{2} x^{4*2} = 100x^8[/tex]

3.

[tex]4^4x^{3*4}y^{2*4} = 256x^{12}y^8[/tex]

4.

[tex]3^3x^{3*3} = 27x^9[/tex]

5.

[tex]6^3x^{2*3} = 216x^6[/tex]

Explanation:

basically, ilagay mo lang yung exponent sa labas ng parentheses dun sa bawat number at variable. kapag ilalagay sa variable, i-multiply mo lang yung exponent na nasa labas dun sa exponent sa loob.

#1

[tex] \green{ \sf{ {(5x}^{5} )}^{3} }[/tex]

Use this property:

[tex] \red{ \sf{ { ({a}^{m}) }^{n} = {a}^{m \times n} }}[/tex]

[tex] \green{ \sf{ {(5x}^{5} )}^{3} = {5x}^{5 \times 3} }[/tex]

[tex] \green{ \sf{ {(5x}^{5} )}^{3} = {5x}^{15} }[/tex]

#2

[tex] \green{ \sf{ {(10x}^{4} )}^{2} }[/tex]

Use this property:

[tex] \red{ \sf{ { ({a}^{m}) }^{n} = {a}^{m \times n} }}[/tex]

[tex] \green{ \sf{ {(10x}^{4} )}^{2} = {10x}^{4 \times 2} }[/tex]

[tex] \green{ \sf{ {(10x}^{4} )}^{2} = {10x}^{8} }[/tex]

#3

[tex] \green{ \sf{ {(4x}^{3} {y}^{2} )}^{4} }[/tex]

Use this property:

[tex] \red{ \sf{ { (a{x}^{m} {y}^{n} ) }^{p} = {a}^{p} \times ({x}^{m} ) ^{p} \times {( {y}^{n}) }^{p} }}[/tex]

[tex] \green{ \sf{ {(4x}^{3} {y}^{2} )}^{4} = {4}^{4} \times ( {x}^{3}) ^{4} \times {( {y}^{2}) }^{4} }[/tex]

[tex] \green{ \sf{ {(4x}^{3} {y}^{2} )}^{4} = 256 \times {x}^{4 \times 3} \times { {y}^{2 \times 4}} }[/tex]

[tex] \green{ \sf{ {(4x}^{3} {y}^{2} )}^{4} = 256 {x}^{12} { {y}^{8}} }[/tex]

#4

[tex] \green{ \sf{ {(3x}^{3} )}^{3} }[/tex]

Use this property:

[tex] \red{ \sf{ { ({a}^{m}) }^{n} = {a}^{m \times n} }}[/tex]

[tex] \green{ \sf{ {(3x}^{3} )}^{3} = {3x}^{3 \times 3} }[/tex]

[tex] \green{ \sf{ {(3x}^{3} )}^{3} = {3x}^{9} }[/tex]

#5

[tex] \green{ \sf{ {(6x}^{2} )}^{3} }[/tex]

Use this property:

[tex] \red{ \sf{ { ({a}^{m}) }^{n} = {a}^{m \times n} }}[/tex]

[tex] \green{ \sf{ {(6x}^{2} )}^{3} = {6x}^{2 \times 3} }[/tex]

[tex] \green{ \sf{ {(6x}^{2} )}^{3} = {6x}^{6} }[/tex]